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Symmetry
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Multi-Criteria Decision Aid methods in fuzzy decision problems – part...
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Multi-Criteria Decision Aid methods in fuzzy decision problems – part II

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: closed (31 March 2021) | Viewed by 104799

Special Issue Editors

Dr. Paweł Ziemba

E-Mail Website1 Website2
Guest Editor
Faculty of Economics, Finance and Management, University of Szczecin, Cukrowa 8, 71-004 Szczecin, Poland
Interests: multi-criteria decision analysis/making; MCDA methods; sustainable management; sustainability assessment; fuzzy sets
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Jarosław Jankowski

E-Mail Website
Guest Editor
Department of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, Szczecin, Poland
Interests: information diffusion; decision support systems; sustainability; human-computer interaction; online marketing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

After the success of the Special Issue “Multi-Criteria Decision Aid methods in fuzzy decision problems” (https://0-www-mdpi-com.brum.beds.ac.uk/journal/symmetry/special_issues/Multi_Criteria_Decision_fuzzy_decision), we are glad to announce the Special Issue “Multi-Criteria Decision Aid methods in fuzzy decision problems – part II”. In the first part of the Special Issue in 2018-2019, we cooperated with excellent scholars/scientific groups and published several important high-level articles which have already been cited according to the data of Web of Science (currently over 110 citations in total) and Scopus (currently over 170 citations in total). Our goal is to increase knowledge and develop the decision sciences in the field of uncertain information, which will make a great contribution to management, sustainability, marketing, etc. Thus, we will continue the Special Issue “Multi-Criteria Decision Aid methods in fuzzy decision problems” as part II.

The notion of symmetry is of particular importance in Multi-Criteria Decision Aid (MCDA). Symmetry, asymmetry and antisymmetry are basic characteristics of binary relations used when modelling the decision maker’s preferences. Moreover, the notion of symmetry appeared in many articles about the fuzzy set theory which is employed in the MCDA methods.

The fuzzy set theory allows capturing uncertainty, imprecision, inaccurate definition of a decision problem and, as a consequence, fuzzing the problem. Fuzzing may include input data representing alternatives, weights of criteria or the decision maker ’s preferences. The first type of fuzzing takes place when the decision maker is not able to precisely evaluate the weights of criteria or the consequences of individual alternatives. The fuzzy MCDA methods deal with this kind of fuzzing. Next, the fuzzing of the decision maker ’s preferences take place when he or she cannot determine how much (if any) one alternative is better than another one with regard to a defined criterion. The decision maker ’s fuzzy preferences are used in some outranking MCDA methods. Furthermore, the fuzzy outranking methods deal with both types of fuzzing.

This Special Issue invites contributions dealing with:

  • the preparation and development of MCDA methods capable of capturing the fuzziness (uncertainty, imprecision and inaccurate definition) of the decision problem,
  • the research into the application of MCDA methods in fuzzy decision problems in the area of management, logistics, sustainability, marketing, finance, electronic markets, social media and others.

Survey and theoretical articles, as well as application papers, are welcome.

References:

1) Perny, P.; Roy, B. The Use of Fuzzy Outranking Relations in Preference Modelling. Fuzzy Sets and Systems 1992, 49, 33-53.

2) Ziemba, P. NEAT F-PROMETHEE – a New Fuzzy Multiple Criteria Decision Making Method Based on the Adjustment of Mapping Trapezoidal Fuzzy Numbers. Expert Systems with Applications 2018, 110, 363-380.

3) Mardani, A.; Jusoh, A.; Zavadskas, E.K. Fuzzy multiple criteria decision-making techniques and applications – Two decades review from 1994 to 2014. Expert Systems with Applications 2015, 42(8), 4126-4148.

Dr. Paweł Ziemba
Prof. Dr. Jarosław Jankowski
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Fuzzy (uncertain, imprecise, ill-determined) decision problems
  • Multi-criteria decision aid
  • fuzzy MCDA methods
  • Fuzzy AHP/ANP
  • Fuzzy TOPSIS
  • Fuzzy DEMATEL
  • Outranking MCDA methods
  • (Fuzzy) PROMETHEE
  • (Fuzzy) ELECTRE
  • Applications of fuzzy MCDA methods
  • Applications of outranking MCDA methods

Published Papers (33 papers)

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23 pages, 469 KiB  
Article
A Cooperative Partner Selection Study of Military-Civilian Scientific and Technological Collaborative Innovation Based on Interval-Valued Intuitionistic Fuzzy Set
by Bing Li and Jihai Zhang
Symmetry 2021, 13(4), 553; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13040553 - 27 Mar 2021
Cited by 11 | Viewed by 1915
Abstract
Military-civilian scientific and technological collaborative innovation (MCSTCI) is an important intersection of civil-military integrated development strategies and innovation-driven development strategies, and has become a brand-new model for Chinese key scientific and technological research. The selection of cooperative partner between military and civilian innovation [...] Read more.
Military-civilian scientific and technological collaborative innovation (MCSTCI) is an important intersection of civil-military integrated development strategies and innovation-driven development strategies, and has become a brand-new model for Chinese key scientific and technological research. The selection of cooperative partner between military and civilian innovation entities is not only the primary segment to carry out MCSTCI activities, but also an important foundation for achieving complementary advantages and win-win cooperation. Therefore, on the basis of summarizing and combing the evaluation indicators, a partner selection model based on interval-valued intuitionistic fuzzy set multi-attribute decision-making is proposed. Firstly, we improve the traditional scoring function, and combine the new scoring function and entropy weight method to determine the weight of each evaluation indicator. Secondly, considering the impact of decision-makers’ risk attitudes, a method of transforming evaluation matrix based on hesitancy distribution is proposed. Finally, the grey correlation and TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method is used to mark and rank the candidates, and the innovation entities with the highest score is selected as the collaborative innovation partner. An example of a military equipment manufacturing enterprise in Beijing for partner selection in order to carry out joint technological research on a certain anti-ship missile weapon shows that the model is more comprehensive and flexible in solving fuzzy multi-attribute decision-making problems, and can assess and select cooperative partners for MCSTCI scientifically and objectively. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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20 pages, 1628 KiB  
Article
A Novel Fuzzy SIMUS Multicriteria Decision-Making Method. An Application in Railway Passenger Transport Planning
by Svetla Stoilova and Nolberto Munier
Symmetry 2021, 13(3), 483; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13030483 - 16 Mar 2021
Cited by 27 | Viewed by 2069
Abstract
To increase the level of adequacy in multi-criteria decision-making in the case of uncertainty, it is essential to reduce the subjectivism and to increase the reality of obtained results. The study aims to propose a novel fuzzy multi-criteria method based on the fuzzy [...] Read more.
To increase the level of adequacy in multi-criteria decision-making in the case of uncertainty, it is essential to reduce the subjectivism and to increase the reality of obtained results. The study aims to propose a novel fuzzy multi-criteria method based on the fuzzy linear programming method and sequential interactive model for urban systems method (SIMUS), named fuzzy SIMUS. This paper is something completely different because it links the power of fuzzy with the advantage of the SIMUS method. Indeed, not using weights, it works with optimal values. Here, this procedure is presented for the first time. The methodology consists of three stages. The first stage includes forming the parameters of a multi-criteria model in the case of uncertainty. The initial matrix has three values: lower, medium, and upper. In the second stage, the fuzzy SIMUS model for each objective is formed based on fuzzy linear programming method. The third stage deals with the ranking of the alternatives. The methodology was experimented for planning railway intercity passenger transport in Bulgarian’s railway network. Nine alternative transport plans and eight criteria were studied. It was found that the objectives which influence ranking the most are the frequency of train stops (15%), direct operational costs (15%), train’s capacity (14.7%), and reliability (14.3%). A transport plan for railway passenger transport is proposed. A verification of the results was performed. It was found that the stability of the choice presented a suitable alternative. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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18 pages, 880 KiB  
Article
Multi-Criteria Decision-Making Methods in Fuzzy Decision Problems: A Case Study in the Frozen Shrimp Industry
by Chia-Nan Wang, Van Thanh Nguyen, Jui-Chung Kao, Chih-Cheng Chen and Viet Tinh Nguyen
Symmetry 2021, 13(3), 370; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13030370 - 25 Feb 2021
Cited by 19 | Viewed by 2920
Abstract
The European Union (EU) is the largest shrimp consumer market in the world in terms of requirements for shrimp product imports. Therefore, other enterprises that export frozen shrimp to the EU must consider many criteria when choosing suppliers of raw shrimp. The difficulty [...] Read more.
The European Union (EU) is the largest shrimp consumer market in the world in terms of requirements for shrimp product imports. Therefore, other enterprises that export frozen shrimp to the EU must consider many criteria when choosing suppliers of raw shrimp. The difficulty of choosing suppliers of raw shrimp makes selecting raw material suppliers in the fisheries sector a multi-criteria decision-making problem. In such problems, the decision makers must review and evaluate many criteria—including qualitative and quantitative factors—to achieve an optimal result. While there have been multiple multi-criteria decision making models developed to support supplier selection processes in different industries, none of these have been developed to solve the particular problems facing the shrimp industry, especially as it concerns a fuzzy decision-making environment. In this research, the authors propose a Multi-Criteria Decision Making model (MCDM) including the Fuzzy Analytical Network Process (FANP) and Weighted Aggregated Sum Product Assessment (WASPAS) for the evaluation and selection process of shrimp suppliers in the fisheries industry. The model is applied to a real-world case study and the results show that Supplier 3 (SA3) is the most optimal supplier of raw shrimp. The contribution of this work is the employment of FANP and WASPAS to propose an MCDM for ranking potential suppliers in the fisheries industry in a fuzzy environment. The proposed approach can also be modified to support complex decision-making processes in fuzzy environments in different industries. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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28 pages, 3192 KiB  
Article
Item Response Theory Models for the Fuzzy TOPSIS in the Analysis of Survey Data
by Bartłomiej Jefmański and Adam Sagan
Symmetry 2021, 13(2), 223; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13020223 - 29 Jan 2021
Cited by 2 | Viewed by 2226
Abstract
The fuzzy TOPSIS (The Technique for Order of Preference by Similarity to Ideal Solution) is an attractive tool for measuring complex phenomena based on uncertain data. The original version of the method assumes that the object assessments in terms of the adopted criteria [...] Read more.
The fuzzy TOPSIS (The Technique for Order of Preference by Similarity to Ideal Solution) is an attractive tool for measuring complex phenomena based on uncertain data. The original version of the method assumes that the object assessments in terms of the adopted criteria are expressed as triangular fuzzy numbers. One of the crucial stages of the fuzzy TOPSIS is selecting the fuzzy conversion scale, which is used to evaluate objects in terms of the adopted criteria. The choice of a fuzzy conversion scale may influence the results of the fuzzy TOPSIS. There is no uniform approach in constructing and selecting the fuzzy conversion scale for the fuzzy TOPSIS. The choice is subjective and made by researchers. Therefore, the aim of the article is to present a new, objective approach to the construction of fuzzy conversion scales based on Item Response Theory (IRT) models. The following models were used in the construction of fuzzy conversion scales: Polychoric Correlation Model (PM), Polytomous Rasch Model (PRM), Rating Scale Model (RSM), Partial Credit Model (PCM), Generalized Partial Credit Model (GPCM), Graded Response Model (GRM), Nominal Response Model (NRM). The usefulness of the proposed approach is presented on the example of the analysis of a survey’s results on measuring the quality of professional life of inhabitants of selected communes in Poland. The obtained results indicate that the choice of the fuzzy conversion scale has a large impact on the closeness coefficient values. A large difference was also observed in the spreads of triangular fuzzy numbers between scales based on IRT models and those used in the literature on the subject. The use of the fuzzy TOPSIS with fuzzy conversion scales built based on PRM, RSM, PCM, GPCM, and GRM models gives results with a greater range of variability than in the case of fuzzy conversion scales used in empirical research. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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21 pages, 861 KiB  
Article
Evaluation of Online Teaching Quality: An Extended Linguistic MAGDM Framework Based on Risk Preferences and Unknown Weight Information
by Hui Lin, Jianxin You and Tao Xu
Symmetry 2021, 13(2), 192; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13020192 - 26 Jan 2021
Cited by 14 | Viewed by 2412
Abstract
Evaluation of online teaching quality has become an important issue because many universities are turning to online classes due to the Corona Virus Disease 2019 (COVID-19) pandemic. In this paper, online teaching quality evaluation is considered as a linguistic multi-attribute group decision-making (MAGDM) [...] Read more.
Evaluation of online teaching quality has become an important issue because many universities are turning to online classes due to the Corona Virus Disease 2019 (COVID-19) pandemic. In this paper, online teaching quality evaluation is considered as a linguistic multi-attribute group decision-making (MAGDM) problem. Generally, the evaluation sematic information can be symmetrically or asymmetrically distributed in linguistic term sets. Thus, an extended linguistic MAGDM framework is proposed for evaluating online teaching quality. As the main contribution, the proposed method takes into account the risk preferences of assessment experts (AEs) and unknown weight information of attributes and sub-attributes. To be specific, the Delphi method is employed to establish a multi-level evaluation indicator system (EIS) of online teaching quality. Then, by introducing the group generalized linguistic term set (GLTS) with two risk preference parameters, a two-stage optimization model is developed to calculate the weights of attributes and sub-attributes objectively. Subsequently, the linguistic MAGDM framework was divided into two stages. The first stage maximizes the group comprehensive rating values of teachers on different attributes to obtain partial ranking results for teachers on each attribute. The latter stage maximizes the group comprehensive rating values of teachers to evaluate the overall quality. Finally, a case study is provided to illustrate how to apply the framework to evaluate online teaching quality. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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25 pages, 6593 KiB  
Article
Pareto Optimal Decisions in Multi-Criteria Decision Making Explained with Construction Cost Cases
by Hubert Anysz, Aleksander Nicał, Željko Stević, Michał Grzegorzewski and Karol Sikora
Symmetry 2021, 13(1), 46; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13010046 - 30 Dec 2020
Cited by 31 | Viewed by 4084
Abstract
In multi-criteria decision-making (MCDM) problems the decision-maker is often forced to accept a not ideal solution. If the ideal choice exists, it would be certainly chosen. The acceptance of a non- ideal solution leads to some inadequate properties in the chosen solution. MCDM [...] Read more.
In multi-criteria decision-making (MCDM) problems the decision-maker is often forced to accept a not ideal solution. If the ideal choice exists, it would be certainly chosen. The acceptance of a non- ideal solution leads to some inadequate properties in the chosen solution. MCDM methods help the decision-maker to structure his needs considering different units, in which the properties of the solutions are expressed. Secondly, with MCDM tools the assessment of the available solutions can be calculated with consideration of the decision-maker’s needs. The incorporation of the cost criterion into the decision maker’s preferences calculation, and the solution assessment calculation, deprives the decision-maker of the ability to calculate the financial result of the decision he must make. A new multi-criteria decision making with cost criterion analysed at the final stage (MCDM-CCAF) method is developed based on principle of Pareto optimal decisions. It is proposed to exclude the cost criterion from the MCDM analysis and consider it at the final phase of the decision-making process. It is illustrated by example solutions with consideration of cost criterion and without it. It is proposed to apply the invented post-processing method to all MCDM analyses where the cost criterion of analysed variants is considered. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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29 pages, 1343 KiB  
Article
Hybrid Hesitant Fuzzy Multi-Criteria Decision Making Method: A Symmetric Analysis of the Selection of the Best Water Distribution System
by Samayan Narayanamoorthy, Veerappan Annapoorani, Samayan Kalaiselvan and Daekook Kang
Symmetry 2020, 12(12), 2096; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12122096 - 17 Dec 2020
Cited by 13 | Viewed by 2785
Abstract
Every country’s influence and livelihood is centered on that country’s water source. Therefore, many studies are being conducted worldwide to improve and sustain water resources. In this research paper, we have selected and researched the water scheme for groundwater recharge and drinking water [...] Read more.
Every country’s influence and livelihood is centered on that country’s water source. Therefore, many studies are being conducted worldwide to improve and sustain water resources. In this research paper, we have selected and researched the water scheme for groundwater recharge and drinking water supply of drought prone areas. The water project is aimed at connecting the drought prone areas of the three districts of Tamil Nadu to filling up the ponds in their respective villages and raising the ground water level and meeting the drinking water requirement. We have chosen a multi-criteria decision method to select the best alternative in a complex situation. When reviewing the implementation of this water project, many experts and people who will benefit from this project may have some hesitation and ambiguity in their suggestion on choosing the best water distribution system.We believe that the benefits of this project can be fully availed of if we choose a water distribution system. Our contribution in this article is to choose the best water distribution system for this project by use of our proposed multi-criteria decision making (MCDM) methods, hesitant fuzzy standard deviation with multi-objective optimization method by ratio analysis (HFSDV-MOORA), hesitant fuzzy standard deviation with technique, for order preference by similarity to an ideal solution (HFSDV-TOPSIS) and hesitant fuzzy standard deviation with VIsekriterijumsko Kompromisno Rangiranje (HFSDV-VIKOR), which will provide the best solution for improving the water resource for the drought-prone areas of three districts. Finally, we have identified and compared the correlation coefficient between proposed methods. As a result of the study, it has been found that the best water supply system is closed concrete pipes laid along agricultural land through the rural areas. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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30 pages, 1382 KiB  
Article
A Distinctive Symmetric Analyzation of Improving Air Quality Using Multi-Criteria Decision Making Method under Uncertainty Conditions
by Samayan Narayanamoorthy, Arumugam Anuja, Daekook Kang, Joseph Varghese Kureethara, Samayan Kalaiselvan and Thangaraj Manirathinam
Symmetry 2020, 12(11), 1858; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12111858 - 11 Nov 2020
Cited by 6 | Viewed by 1955
Abstract
This world has a wide range of technologies and possibilities that are available to control air pollution. Still, finding the best solution to control the contamination of the air without having any impact on humans is a complicated task. This proposal helps to [...] Read more.
This world has a wide range of technologies and possibilities that are available to control air pollution. Still, finding the best solution to control the contamination of the air without having any impact on humans is a complicated task. This proposal helps to improve the air quality using the multi-criteria decision making method. The decision to improve air quality is a challenging problem with today’s technology and environmental development level. The multi-criteria decision making method is quite often faced with conditions of uncertainty, which can be tackled by employing fuzzy set theory. In this paper, based on an objective weighting method (CCSD), we explore the improved fuzzy MULTIMOORA approach. We use the classical Interval-Valued Triangular Fuzzy Numbers (IVTFNs), viz. the symmetric lower and upper triangular numbers, as the basis. The triangular fuzzy number is identified by the triplets; the lowest, the most promising, and the highest possible values, symmetric with respect to the most promising value. When the lower and upper membership functions are equated to one, we get the normalized interval-valued triangular fuzzy numbers, which consist of symmetric intervals. We evaluate five alternatives among the four criteria using an improved MULTIMOORA method and select the best method for improving air quality in Tamil Nadu, India. Finally, a numerical example is illustrated to show the efficiency of the proposed method. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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20 pages, 1374 KiB  
Article
Hesitant Fuzzy Sets Based Symmetrical Model of Decision-Making for Estimating the Durability of Web Application
by Kavita Sahu, Fahad A. Alzahrani, R. K. Srivastava and Rajeev Kumar
Symmetry 2020, 12(11), 1770; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12111770 - 26 Oct 2020
Cited by 84 | Viewed by 2222
Abstract
The development of web applications essentially relies on users’ demands who expect highly efficacious but cost effective software services. Managing time and cost so as to develop web applications that cater to the users’ need is a challenge for developers at present. Moreover, [...] Read more.
The development of web applications essentially relies on users’ demands who expect highly efficacious but cost effective software services. Managing time and cost so as to develop web applications that cater to the users’ need is a challenge for developers at present. Moreover, low-cost maintenance can only be achieved by enhancing the durability of the web applications. Identifying characteristics of durability is a complex task because the different experts have different opinions regarding the significance of characteristics that determine durability quotient of the web applications. As established by the best practices undertaken in this context, some experts consider quality to be the most important factor for determining durability. Therefore, the present study enlists multi-criteria decision-based symmetrical technique to address the multi-vector option availability for the apt selection of the characteristics for durability. Furthermore, it has also been identified that a numerical assessment of web applications’ durability can affect the service life and low-cost management in web applications. In this context, to achieve high durability and longevity in web applications, this paper attempts to illustrate and perform a numerical evaluation of durability characteristics. By understanding the various characteristics and their significance towards durability, the paper finds that the hesitant fuzzy-based symmetrical technique of the Analytic Hierarchy Process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is an effective methodology for evaluating web applications’ durability. For evaluating the quality of the results and establishing their sensitivity, the authors have assessed the outcomes on six different projects of the University. Additionally, results assessed and discussed in this paper would be a conclusive reference for the developers in their attempts to develop highly durable and manageable web applications. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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34 pages, 414 KiB  
Article
On Application Oriented Fuzzy Numbers for Imprecise Investment Recommendations
by Anna Łyczkowska-Hanćkowiak
Symmetry 2020, 12(10), 1672; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12101672 - 13 Oct 2020
Cited by 9 | Viewed by 1436
Abstract
The subtraction of fuzzy numbers (FNs) is not an inverse operator to FNs addition. The family of all oriented FNs (OFNs) may be considered as symmetrical closure of all the FNs family in that the subtraction is an inverse operation to addition. An [...] Read more.
The subtraction of fuzzy numbers (FNs) is not an inverse operator to FNs addition. The family of all oriented FNs (OFNs) may be considered as symmetrical closure of all the FNs family in that the subtraction is an inverse operation to addition. An imprecise present value is modelled by a trapezoidal oriented FN (TrOFN). Then, the expected discount factor (EDF) is a TrOFFN too. This factor may be applied as a premise for invest-making. Proposed decision strategies are dependent on a comparison of an oriented fuzzy profit index and the specific profitability threshold. This way we get an investment recommendation described as a fuzzy subset on the fixed rating scale. Risk premium measure is a special case of profit index. Further in the paper, the Sharpe’s ratio, the Jensen’s ratio, the Treynor’s ratio, the Sortino’s ratio, Roy’s criterion and the Modiglianis’ coefficient are generalised for the case when an EDF is given as a TrOFN. In this way, we get many different imprecise recommendations. For this reason, an imprecise recommendation management module is described. Obtained results show that the proposed theory can be used as a theoretical background for financial robo-advisers. All theoretical considerations are illustrated by means of a simple empirical case study. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
19 pages, 1242 KiB  
Article
Fuzzy Model Identification Using Monolithic and Structured Approaches in Decision Problems with Partially Incomplete Data
by Andrii Shekhovtsov, Joanna Kołodziejczyk and Wojciech Sałabun
Symmetry 2020, 12(9), 1541; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091541 - 18 Sep 2020
Cited by 35 | Viewed by 1936
Abstract
A significant challenge in the current trend in decision-making methods is the problem’s class in which the decision-maker makes decisions based on partially incomplete data. Classic methods of multicriteria decision analysis are used to analyze alternatives described by using numerical values. At the [...] Read more.
A significant challenge in the current trend in decision-making methods is the problem’s class in which the decision-maker makes decisions based on partially incomplete data. Classic methods of multicriteria decision analysis are used to analyze alternatives described by using numerical values. At the same time, fuzzy set modifications are usually used to include uncertain data in the decision-making process. However, data incompleteness is something else. In this paper, we show two approaches to identify fuzzy models with partially incomplete data. The monolithic approach assumes creating one model that requires many queries to the expert. In the structured approach, the problem is decomposed into several interrelated models. The main aim of the work is to compare their accuracy empirically and to determine the sensitivity of the obtained model to the used criteria. For this purpose, a study case will be presented. In order to compare the proposed approaches and analyze the significance of the decision criteria, we use two ranking similarity coefficients, i.e., symmetric rw and asymmetric WS. In this work, the limitations of each approach are presented, and the results show great similarity despite the use of two structurally different approaches. Finally, we show an example of calculations performed for alternatives with partially incomplete data. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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23 pages, 1002 KiB  
Article
Role of Ergonomic Factors Affecting Production of Leather Garment-Based SMEs of India: Implications for Social Sustainability
by Koppiahraj Karuppiah, Bathrinath Sankaranarayanan, Syed Mithun Ali and Golam Kabir
Symmetry 2020, 12(9), 1414; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091414 - 25 Aug 2020
Cited by 21 | Viewed by 5653
Abstract
This paper aims to identify, evaluate, and measure the ergonomic factors hampering the production of leather garment-based small and medium-sized enterprises (SMEs). Ergonomic problems faced by the workers largely impact the health of individuals and also the productivity of a firm. Based on [...] Read more.
This paper aims to identify, evaluate, and measure the ergonomic factors hampering the production of leather garment-based small and medium-sized enterprises (SMEs). Ergonomic problems faced by the workers largely impact the health of individuals and also the productivity of a firm. Based on experts’ opinions and a literature survey, three emerging categories—namely, occupational disease, personal factors, and the industrial environment—with a total of twenty factors were identified to examine symmetrical impact in five leather garment companies. In this research work, Cronbach’s α was evaluated to check the validity of the ergonomic factors identified through the literature survey. Then, using the fuzzy analytic hierarchy process (FAHP), the identified ergonomic factors were evaluated. A sensitivity analysis was carried out to validate the robustness of the results obtained using the integrated approach. Outdated machinery, vibration, operational setup, fatigue, and poor ventilation and lighting are the top five factors inducing ergonomic-related problems and hampering the production of the leather garment companies in India. These top ergonomic factors are the result of a failure in the provision of an ambient working environment. Providing ergonomically designed working environments may lower the occurrence of ergonomic problems. The findings of this study will assist industrial managers to enhance production rate and to progress towards social sustainability in Indian SMEs. The proposed symmetrical assessment in this study could also be considered as a benchmark for other companies in which human–machine interaction is significant. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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19 pages, 6537 KiB  
Article
Evaluation and Balance of Cognitive Friction: Evaluation of Product Target Image Form Combining Entropy and Game Theory
by Kai Qiu, Jianning Su, Xinxin Zhang and Wenjin Yang
Symmetry 2020, 12(9), 1398; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091398 - 21 Aug 2020
Cited by 9 | Viewed by 2418
Abstract
With the great progress of product development technology, product forms have been greatly enriched by cognitive differences; users and designers have formed a “cognitive friction” phenomenon in the product evaluation process, which results in designers being unable to grasp user emotions accurately and [...] Read more.
With the great progress of product development technology, product forms have been greatly enriched by cognitive differences; users and designers have formed a “cognitive friction” phenomenon in the product evaluation process, which results in designers being unable to grasp user emotions accurately and risks of product development failure. This paper aims to balance the cognitive differences between cognitive subjects (users and designers) and evaluates the product image form. First, image entropy is used to evaluate and extract the weight of the product target image. Second, fuzzy Theil entropy is used to evaluate the cognitive friction between cognitive subjects, and its existence and size are visually presented. Then, a cognitive friction balance model is built by combining game theory, the comprehensive evaluation weight between cognitive subjects is obtained, and the product image form is ranked and optimized. Finally, all the research steps are described in the form of a household hair dryer. The results show that fuzzy Theil entropy and game theory have significant advantages in the evaluation and balance of cognitive friction in product design. Thus, the cognitive friction evaluation and balance model constructed from the fuzzy Theil entropy and game theory do not only enable different cognitive subjects to achieve cognitive symmetry, but also screen out product forms that meet the cognitive needs of users. This finding provides the theoretical basis and practical significance for the establishment of a closed-loop model in cognitive friction balance and the reduction of cognitive differences between cognitive subjects in the entire process of product design. It also introduces new ways of thinking and methods for cognitive science research. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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14 pages, 276 KiB  
Article
Fuzzy Analytic Hierarchy Process-Based Multi-Criteria Decision Making for Universities Ranking
by Rashad Aliyev, Hasan Temizkan and Rafig Aliyev
Symmetry 2020, 12(8), 1351; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081351 - 12 Aug 2020
Cited by 22 | Viewed by 4417
Abstract
High competition between universities has been increasing over the years, and stimulates higher education institutions to attain higher positions in the ranking list. Ranking is an important performance indicator of university status evaluation, and therefore plays an essential role in students’ university selection. [...] Read more.
High competition between universities has been increasing over the years, and stimulates higher education institutions to attain higher positions in the ranking list. Ranking is an important performance indicator of university status evaluation, and therefore plays an essential role in students’ university selection. The ranking of universities has been carried out using different techniques. Main goal of decision processes in real-life problems is to deal with the symmetry or asymmetry of different types of information. We consider that multi-criteria decision making (MCDM) is well applicable to symmetric information modelling. Analytic hierarchy process (AHP) is a well-known technique of MCDM discipline, and is based on pairwise comparisons of criteria/alternatives for alternatives’ evaluation. Unfortunately, the classical AHP method is unable to deal with imprecise, vague, and subjective information used for the decision making process in complex problems. So, introducing a more advanced tool for decision making under such circumstances is inevitable. In this paper, fuzzy analytic hierarchy process (FAHP) is applied for the comparison and ranking of performances of five UK universities, according to four criteria. The criteria used for the evaluation of universities’ performances are teaching, research, citations, and international outlook. It is proven that applying FAHP approach makes the system consistent, and by the calculation of coefficient of variation for all alternatives, it becomes possible to rank them in prioritized order. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
27 pages, 8042 KiB  
Article
Fuzzy TOPSIS-EW Method with Multi-Granularity Linguistic Assessment Information for Emergency Logistics Performance Evaluation
by Yanwu Liu, Liang Li, Yan Tu and Yanlan Mei
Symmetry 2020, 12(8), 1331; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081331 - 10 Aug 2020
Cited by 16 | Viewed by 2693
Abstract
The operation of emergency logistics plays a prominent role in reducing the consequences of disasters. Based on the establishment of a comprehensive evaluation system with the whole period of the disaster cycle that covers emergency preparation, response, and recovery, this paper proposes a [...] Read more.
The operation of emergency logistics plays a prominent role in reducing the consequences of disasters. Based on the establishment of a comprehensive evaluation system with the whole period of the disaster cycle that covers emergency preparation, response, and recovery, this paper proposes a fuzzy-symmetrical Technique for Order Preference by Similarity to Ideal Solution-Entropy Weight (TOPSIS-EW) method with multi-granularity linguistic assessment (MGLA) information to evaluate the performance of emergency logistics. Furthermore, the proposed evaluation method is employed to evaluate the performance of emergency logistics in Wenchuan earthquake, five worst-hit regions (i.e., Wenchuan County, Beichuan County, Qingchuan County, Mianzhu City, Shifang City) were ranked as V, III, I, II, IV, respectively. Finally, the effectiveness and reliability of the method are verified by comparison with the other two related methods and a sensitivity analysis. Based on the comprehensive evaluation results, some specific managerial suggestions are proposed to improve the emergency logistics capacity. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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20 pages, 1914 KiB  
Article
An Integrated Approach of Analytic Hierarchy Process and Triangular Fuzzy Sets for Analyzing the Park-and-Ride Facility Location Problem
by Jairo Ortega, János Tóth, Sarbast Moslem, Tamás Péter and Szabolcs Duleba
Symmetry 2020, 12(8), 1225; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081225 - 26 Jul 2020
Cited by 22 | Viewed by 2829
Abstract
A park and ride (P&R) system is a set of facilities where private vehicle users can transfer to public transport to complete their journey. The main advantage of the system is reducing the congestions problem in the central business district (CBD). Thus, the [...] Read more.
A park and ride (P&R) system is a set of facilities where private vehicle users can transfer to public transport to complete their journey. The main advantage of the system is reducing the congestions problem in the central business district (CBD). Thus, the notion of symmetry is particularly important in multi-criteria decision aid (MCDA) because they are basic characteristics of the binary relationships used in modelling the preferences of decision-makers. The focal point of this study is evaluating the P&R facility system location problem from the experts’ point of view. For this aim, an integrated multicriteria decision-making (MCDM) methodology is proposed to evaluate the location of the facilities of the P&R system. The questionnaire survey was designed and estimated by 10 transport experts in the related field. The famous analytic hierarchy process (AHP) was adopted in a fuzzy environment, where the fuzzy sets have an efficient ability to manage the vague concepts in a specific way; moreover, it can mitigate the evaluator reasoning during decision-making. The hierarchical structure of the problem was established to evaluate a real-life problem in Cuenca city, Ecuador. The outcomes highlighted the “accessibility of public transport” as the most significant issue in the P&R facility location problem. The obtained results provide more flexible facilities than the pure AHP method. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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33 pages, 2981 KiB  
Article
Assessing and Prioritizing the Climate Change Policy Objectives for Sustainable Development in Pakistan
by Waqas Ahmed, Qingmei Tan, Ghulam Muhammad Shaikh, Hamid Waqas, Nadeem Ahmed Kanasro, Sharafat Ali and Yasir Ahmed Solangi
Symmetry 2020, 12(8), 1203; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081203 - 22 Jul 2020
Cited by 29 | Viewed by 8765
Abstract
The world is facing the observable and direct impacts of climate change in the shape of extreme weather events, irregular precipitation, glacial melt, sea-level rise, an asymmetric average temperature trends, higher oceanic temperatures, damage to natural ecosystems, and biodiversity. In 2015, collective wisdom [...] Read more.
The world is facing the observable and direct impacts of climate change in the shape of extreme weather events, irregular precipitation, glacial melt, sea-level rise, an asymmetric average temperature trends, higher oceanic temperatures, damage to natural ecosystems, and biodiversity. In 2015, collective wisdom stirred the global community to agree upon two unprecedented milestones in recent human history—the Paris agreement and sustainable development goals (SDGs). The twin global agreements set a platform for collective efforts to secure socio-economic and climatic sustainability. Pakistan also joined the board to put forth policy interventions for the mitigation and adaption of climate change risks to maintain symmetry between the environmental quality and economic development. The government of Pakistan (GOP) formulated the National Climate Change Policy (NCCP (2012)) and passed the Pakistan Climate Change Act (PCCA (2017)) to provide an impetus for the implementation of the NCCP. Yet, an appropriate assessment and prioritization of the objectives of the NCCP are indispensable for productive and effective policies to achieve the targets. This study serves this purpose by prioritizing the climate change policy objectives (CCPOs) based on symmetric principles, i.e., energy, transport, urban and town planning, industry, and agriculture as criteria, with 17 sub-criteria in total. The fuzzy analytical hierarchy process (AHP) results show that the energy sector is the most pivotal while implementing the NCCP. Energy production is the most critical area that needs mitigation policy intervention for shifting the energy mix of the economy from high-carbon to low-carbon energy. The fuzzy AHP analysis further revealed the railway, population and urbanization, air pollution, crop growing practices and techniques as the most important related to transport, urban planning, industry, and agriculture sub-criteria, respectively. The fuzzy VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) analysis showed the ranking of the CCPOs from high to low through the integration of policies, institutional capacity building, water security, natural resource management, natural disaster management, environmental financial structure development, and social sector development. The findings of the present research would be helpful for experts and policymakers to re-examine the NCCP and put forth action plans to achieve sustainable climate and SDGs. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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30 pages, 457 KiB  
Article
The Renewable Energy Source Selection by Remoteness Index-Based VIKOR Method for Generalized Intuitionistic Fuzzy Soft Sets
by Muhammad Jabir Khan, Poom Kumam, Nasser Aedh Alreshidi, Nusrat Shaheen, Wiyada Kumam, Zahir Shah and Phatiphat Thounthong
Symmetry 2020, 12(6), 977; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12060977 - 08 Jun 2020
Cited by 27 | Viewed by 2713
Abstract
In this paper, we introduce the Euclidean, Hamming, and generalized distance measures for the generalized intuitionistic fuzzy soft sets (GIFSSs). We discuss the properties of the presented distance measures. The numerical example of decision making and pattern recognition is discussed based on the [...] Read more.
In this paper, we introduce the Euclidean, Hamming, and generalized distance measures for the generalized intuitionistic fuzzy soft sets (GIFSSs). We discuss the properties of the presented distance measures. The numerical example of decision making and pattern recognition is discussed based on the proposed distance measures. We develop a remoteness index-based VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method for GIFSSs. The displaced and fixed ideals intuitionistic fuzzy values (IFVs) are defined. The novel concept of displaced and fixed remoteness indexes for IFVs are discussed. We discuss the methods to obtain the precise and intuitionistic fuzzy (IF) weights. The several displaced and fixed ranking indexes are defined based on the precise and IF weights. The remoteness indexes based VIKOR methods are proposed in the form of four algorithms. In the end, the selection of renewable energy sources problem is solved by using the four remoteness index-based VIKOR methods. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
15 pages, 2014 KiB  
Article
An Interactive Decision-Making Method for Third-Party Logistics Provider Selection under Hybrid Multi-Criteria
by Yumin Liu, Peng Zhou, Liyuan Li and Feng Zhu
Symmetry 2020, 12(5), 729; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12050729 - 04 May 2020
Cited by 16 | Viewed by 2472
Abstract
Due to the complexity and uncertainty of third-party logistics (3PL) provider selection circumstances, the research on the hybrid multi-criteria decision-making (HMCDM) method with fuzzy hesitation information is becoming more and more important. Based on symmetry principles, both the objectivity of the decision information [...] Read more.
Due to the complexity and uncertainty of third-party logistics (3PL) provider selection circumstances, the research on the hybrid multi-criteria decision-making (HMCDM) method with fuzzy hesitation information is becoming more and more important. Based on symmetry principles, both the objectivity of the decision information and the subjectivity of decision makers’ (DMs) preferences should be considered in the HMCDM method. In this paper, a novel interactive decision-making method to deal with the 3PL provider selection problem of hesitant fuzzy sets, intuitionistic fuzzy sets and real numbers is developed. We first investigate the positive and negative ideal solutions of the alternative and the satisfaction degree of the DMs under hybrid multi-criteria circumstances. Then, the interactive HMCDM models based on satisfaction degrees are established, which can use objective decision information to rank alternatives and, symmetrically, the preference information of the DMs is also taken into account. DMs can modify their preference information using the models and thus make the most reasonable selection of 3PL provider. Finally, the case analysis and sensitivity analysis show that the change of parameter and the setting of the satisfaction lower limit will not affect the optimal rank of alternatives, and the feasibility of the proposed method is confirmed. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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21 pages, 1466 KiB  
Article
Software Security Estimation Using the Hybrid Fuzzy ANP-TOPSIS Approach: Design Tactics Perspective
by Alka Agrawal, Adil Hussain Seh, Abdullah Baz, Hosam Alhakami, Wajdi Alhakami, Mohammed Baz, Rajeev Kumar and Raees Ahmad Khan
Symmetry 2020, 12(4), 598; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12040598 - 09 Apr 2020
Cited by 34 | Viewed by 3241
Abstract
Increasing the number of threats against software vulnerabilities and rapidly growing data breaches have become a key concern for both the IT industry and stakeholders. Developing secure software systems when there is a high demand for software products from individuals as well as [...] Read more.
Increasing the number of threats against software vulnerabilities and rapidly growing data breaches have become a key concern for both the IT industry and stakeholders. Developing secure software systems when there is a high demand for software products from individuals as well as the organizations is in itself a big challenge for the designers and developers. Meanwhile, adopting traditional and informal learnings to address security issues of software products has made it easier for cyber-criminals to expose software vulnerabilities. Hence, it is imperative for the security practitioners to employ a symmetric mechanism so as to achieve the desired level of software security. In this context, a decision-making approach is the most symmetrical technique to assess the security of software in security tactics perspective. Since the security tactics directly address the quality attribute concerns, this symmetric approach will be highly effective in making the software systems more secure. In this study, the authors have selected three main attributes and fifteen sub-attributes at level 1 and level 2, respectively, with ten different software of an institute as alternatives. Furthermore, this study uses a fuzzy-based symmetrical decision-making approach to assess the security of software with respect to tactics. Fuzzy Analytic Network Process (F-ANP) is applied to evaluate the weights of criteria and fuzzy-Symmetrical technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is used to determine impact of alternatives. The proposed symmetrical assessment in this study will be beneficial for both the designers and developers to categorize and prioritize the security attributes and understand the importance of security tactics during software development life cycle. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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16 pages, 519 KiB  
Article
A New Method to Support Decision-Making in an Uncertain Environment Based on Normalized Interval-Valued Triangular Fuzzy Numbers and COMET Technique
by Shahzad Faizi, Wojciech Sałabun, Samee Ullah, Tabasam Rashid and Jakub Więckowski
Symmetry 2020, 12(4), 516; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12040516 - 02 Apr 2020
Cited by 72 | Viewed by 4137
Abstract
Multi-criteria decision-making (MCDM) plays a vibrant role in decision-making, and the characteristic object method (COMET) acts as a powerful tool for decision-making of complex problems. COMET technique allows using both symmetrical and asymmetrical triangular fuzzy numbers. The COMET technique is immune to the [...] Read more.
Multi-criteria decision-making (MCDM) plays a vibrant role in decision-making, and the characteristic object method (COMET) acts as a powerful tool for decision-making of complex problems. COMET technique allows using both symmetrical and asymmetrical triangular fuzzy numbers. The COMET technique is immune to the pivotal challenge of rank reversal paradox and is proficient at handling vagueness and hesitancy. Classical COMET is not designed for handling uncertainty data when the expert has a problem with the identification of the membership function. In this paper, symmetrical and asymmetrical normalized interval-valued triangular fuzzy numbers (NIVTFNs) are used for decision-making as the solution of the identified challenge. A new MCDM method based on the COMET method is developed by using the concept of NIVTFNs. A simple problem of MCDM in the form of an illustrative example is given to demonstrate the calculation procedure and accuracy of the proposed approach. Furthermore, we compare the solution of the proposed method, as interval preference, with the results obtained in the Technique for Order of Preference by Similarity to Ideal solution (TOPSIS) method (a certain preference number). Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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22 pages, 3026 KiB  
Article
A Unified Fuzzy-Based Symmetrical Multi-Criteria Decision-Making Method for Evaluating Sustainable-Security of Web Applications
by Alka Agrawal, Mamdouh Alenezi, Rajeev Kumar and Raees Ahmad Khan
Symmetry 2020, 12(3), 448; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12030448 - 11 Mar 2020
Cited by 14 | Viewed by 2423
Abstract
Although security is an integral aspect of any web application’s growth, sustainability is also a pivotal factor in maintaining the web application. It is clear that the software industry aims to develop different methods and initiatives for achieving high security while maintaining high [...] Read more.
Although security is an integral aspect of any web application’s growth, sustainability is also a pivotal factor in maintaining the web application. It is clear that the software industry aims to develop different methods and initiatives for achieving high security while maintaining high sustainability. Unfortunately, web application protection is useless if the sustainability is low. Thus, the present day need calls for innovation in developing web applications that afford sustainable-security to the users. By improving sustainability along with web application protection, underlying security and sustainability attributes play a vital role in determining the symmetrical effect of the sustainability and security attribute to achieve the best outcome. Sustainability evaluation, therefore, uses security and sustainability qualities to achieve the desired sustainability security solutions. In this study, ten consecutive versions of two web applications were used to determine symmetrical sustainability. The authors used the Fuzzy Analytic Hierarchy Process (Fuzzy-AHP) mechanism to determine sustainability goals and long-term impact. Furthermore, the effect of security on sustainability is assessed, and vice versa. The findings in the paper will prove to be valuable for improving sustainability of the web application. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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13 pages, 1008 KiB  
Article
Poverty Measure Based on Hesitant Fuzzy Decision Algorithm under Social Network Media
by Suwei Gao and Kaiyang Sun
Symmetry 2020, 12(3), 384; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12030384 - 03 Mar 2020
Cited by 3 | Viewed by 3019
Abstract
This study aims to solve the problem that the traditional method of measuring the poverty level in rural and urban areas of China from a purely monetary perspective can’t comprehensively analyze and reflect the poverty. In this study, a multidimensional poverty measurement model [...] Read more.
This study aims to solve the problem that the traditional method of measuring the poverty level in rural and urban areas of China from a purely monetary perspective can’t comprehensively analyze and reflect the poverty. In this study, a multidimensional poverty measurement model with non-monetary indicators is proposed, the data of families and their members provided by the China Health and Nutrition Survey (CHNS) of a certain year’s health and nutrition survey in China are used for analysis, and a fuzzy set method is adopted to analyze the poverty situation in various regions of China. First, the fuzzy function set method is used to calculate the one-dimensional poverty index. On the basis of income, the multi-dimensional poverty fuzzy index is calculated from five dimensions, including education, health, assets, and living standard. The calculation results of the single-dimensional poverty and the multi-dimensional poverty are compared to further analyze the reasons of the family poverty of rural residents. Second, the poverty rate of each dimension in each region is calculated by referring to the appropriate measurement indexes of each dimension of the message passing interface (MPI) team. The results show that the concept of measuring poverty by the fuzzy set method is more sensitive to the overall distribution of population in the poverty dimension than the poverty line method. Compared with the poverty line method, the fuzzy set method can better consider the overall distribution of population in poverty dimension. Accordingly, China should strengthen the infrastructure construction in rural areas, increase the investment in education in rural areas, and improve the overall quality of the poor population. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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27 pages, 888 KiB  
Article
Fuzzy Decision Support Modeling for Hydrogen Power Plant Selection Based on Single Valued Neutrosophic Sine Trigonometric Aggregation Operators
by Shahzaib Ashraf, Saleem Abdullah, Shouzhen Zeng, Huanhuan Jin and Fazal Ghani
Symmetry 2020, 12(2), 298; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12020298 - 19 Feb 2020
Cited by 44 | Viewed by 2955
Abstract
In recent decades, there has been a massive growth towards the prime interest of the hydrogen energy industry in automobile transportation fuel. Hydrogen is the most plentiful component and a perfect carrier of energy. Generally, evaluating a suitable hydrogen power plant site is [...] Read more.
In recent decades, there has been a massive growth towards the prime interest of the hydrogen energy industry in automobile transportation fuel. Hydrogen is the most plentiful component and a perfect carrier of energy. Generally, evaluating a suitable hydrogen power plant site is a complex selection of multi-criteria decision-making (MCDM) problem concerning proper location assessment based on numerous essential criteria, the decision-makers expert opinion, and other qualitative/quantitative aspects. This paper presents the novel single-valued neutrosophic (SVN) multi-attribute decision-making method to help decision-makers choose the optimal hydrogen power plant site. At first, novel operating laws based on sine trigonometric function for single-valued neutrosophic sets (SVNSs) are introduced. The well-known sine trigonometry function preserves the periodicity and symmetric in nature about the origin, and therefore it satisfies the decision-maker preferences over the multi-time phase parameters. In conjunction with these properties and laws, we define several new aggregation operators (AOs), called SVN weighted averaging and geometric operators, to aggregate SVNSs. Subsequently, on the basis of the proposed AOs, we introduce decision-making technique for addressing multi-attribute decision-making (MADM) problems and provide a numerical illustration of the hydrogen power plant selection problem for validation. A detailed comparative analysis, including a sensitivity analysis, was carried out to improve the understanding and clarity of the proposed methodologies in view of the existing literature on MADM problems. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
28 pages, 1021 KiB  
Article
Probabilistic Hybrid Linguistic Approaches for Multiple Attribute Group Decision Making with Decision Hesitancy and the Prioritization of Attribute Relationships
by Junling Zhang, Ying Hong, Xiaowen Qi and Changyong Liang
Symmetry 2020, 12(2), 235; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12020235 - 04 Feb 2020
Cited by 3 | Viewed by 1845
Abstract
Focusing on ill-structured multiple attribute decision-making (MADM) problems, including decision hesitancy and attribute prioritization relationships, this paper investigates appropriate approaches for decision making. Firstly, we introduce the probabilistic hybrid linguistic term set (P-HLTS) for capturing probabilistic preferences about possible linguistic labels belonging to [...] Read more.
Focusing on ill-structured multiple attribute decision-making (MADM) problems, including decision hesitancy and attribute prioritization relationships, this paper investigates appropriate approaches for decision making. Firstly, we introduce the probabilistic hybrid linguistic term set (P-HLTS) for capturing probabilistic preferences about possible linguistic labels belonging to a wide range of hesitant linguistic term sets. Entropy and distance measurements for P-HLTS are developed without arbitrary complementing operations. To facilitate decision making with attribute prioritization relationships, we present a probabilistic uncertain balanced linguistic-prioritized weighted average (PUBL-PWA) operator and the probabilistic uncertain balanced linguistic-induced prioritized ordered weighted average (PUBL-IPOWA) operator. In terms of the strength of the above tools, we further construct two multiple attribute group decision-making (MAGDM) approaches under P-HLTS environments, namely, an approach for decision-making situations where attribute prioritization relationships are known in advance and the relative importance of decision makers (DMs) or decision-making units (DMUs) is not required for consideration, and second approach for decision-making situations where both attribute prioritization relationships and the weighted vectors of DMs or DMUs are explicitly unknown. In general, our proposed approaches are more flexible and practical when considering heterogeneous opinions, avoiding information distortion brought about by complementing operation-based distance measures. Furthermore, illustrative application studies are conducted to verify our developed approaches. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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12 pages, 970 KiB  
Article
A Hybrid Fuzzy Analytic Hierarchy Process and the Technique for Order of Preference by Similarity to Ideal Solution Supplier Evaluation and Selection in the Food Processing Industry
by Chia-Nan Wang, Hsiung-Tien Tsai, Van Thanh Nguyen, Viet Tinh Nguyen and Ying-Fang Huang
Symmetry 2020, 12(2), 211; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12020211 - 02 Feb 2020
Cited by 14 | Viewed by 2863
Abstract
Selecting suppliers plays an important role in improving efficiency of supply chains. In the field of extraction of vegetable oil, one of the main submaterials is hexane solvent. Choosing a supplier of hexane solvent is a multicriteria decision-making task that decision-makers must have [...] Read more.
Selecting suppliers plays an important role in improving efficiency of supply chains. In the field of extraction of vegetable oil, one of the main submaterials is hexane solvent. Choosing a supplier of hexane solvent is a multicriteria decision-making task that decision-makers must have an understanding of the quantitative and qualitative elements for assessing the symmetrical impact of the criteria to reach the most accurate result. In this paper, the authors suggest a multicriteria decision-making (MCDM) model for N-hexane solvent (C6H14) supplier evaluation and selection for vegetable oil production. All criteria affecting to the hexane solvent supplier evaluation and selection process are defined by experts. Then, a fuzzy analytic hierarchy process (FAHP) multicriteria comparative analysis method has been applied for determining the weight of all criteria. Finally, the technique for order of preference by similarity to ideal solution (TOPSIS) was applied to select the optimal hexane solvent supplier. As a result, decision making unit 003 (DMU3) is the optimal supplier. The contribution of this research is to propose an MCDM model for hexane solvent supplier selection in the food industry. The work also proposed a useful guideline for supplier evaluation and selection processes in other industries. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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18 pages, 2775 KiB  
Article
A Consensus Measure of Expert Judgment in the Fuzzy TOPSIS Method
by Paweł Ziemba, Aneta Becker and Jarosław Becker
Symmetry 2020, 12(2), 204; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12020204 - 01 Feb 2020
Cited by 26 | Viewed by 3241
Abstract
In the case of many complex, real-world decision problems solved with the participation of a group of experts, it is important to capture the uncertainty of opinions and preferences expressed. In such situations, one can use many modifications of the technique for order [...] Read more.
In the case of many complex, real-world decision problems solved with the participation of a group of experts, it is important to capture the uncertainty of opinions and preferences expressed. In such situations, one can use many modifications of the technique for order preference by similarity to the ideal solution (TOPSIS) method, for example, based on fuzzy numbers. In fuzzy TOPSIS, two aggregation methods of fuzzy expert opinions dominate, the first based on the average value technique and the second one extended by the minimum and maximum functions for determining the support of the aggregated fuzzy number. An important disadvantage of both techniques is the fact that the agreement degree of expert opinions is not taken into account. This article proposes the inclusion of the modified procedure for aggregating individual expert opinions, taking into account the degree of agreement of their opinions (called the similarity aggregation method—SAM) and the ranking of experts into the fuzzy TOPSIS method. The fuzzy TOPSIS method extended in this way was used to solve the decision problem of recruiting employees by a group of experts. As part of the solution, the modified SAM was compared with aggregation procedures based on the average value and min-max (minimum and maximum) support. The results of the conducted research indicate that SAM allows fuzzy numbers to be obtained, characterized by less imprecision and greater stability than the other two considered aggregation procedures. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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19 pages, 1109 KiB  
Article
A Hybrid MCDM Model to Select Optimal Hosts of Variety Shows in the Social Media Era
by Lee-Chun Wu, Kuei-Lun Chang and Sen-Kuei Liao
Symmetry 2020, 12(1), 125; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12010125 - 08 Jan 2020
Cited by 13 | Viewed by 3296
Abstract
The selection of the optimal variety show hosts is a key to television stations. However, no study has a deal with this issue. In this paper, a hybrid multiple criteria decision-making (MCDM) model based on the fuzzy Delphi method, decision-making trial and evaluation [...] Read more.
The selection of the optimal variety show hosts is a key to television stations. However, no study has a deal with this issue. In this paper, a hybrid multiple criteria decision-making (MCDM) model based on the fuzzy Delphi method, decision-making trial and evaluation laboratory (DEMATEL), analytic network process (ANP), and technique for order preference by similarity to ideal solution (TOPSIS) to choose optimal hosts of variety shows for television stations in the social media era was developed. The fuzzy Delphi method was taken as a screening tool for the selection criteria of variety show hosts. Then, DEMATEL was applied to verify the interdependencies between the perspectives. According to the interdependencies, ANP was employed to obtain weights. Finally, TOPSIS ranked the alternatives. The selection criteria were gathered from previous researches and discussions with senior executives of television stations. By the fuzzy Delphi method, 12 criteria were identified. Based on the past study and consultations with four senior executives, we classified 12 essential criteria into four perspectives to develop the hierarchy for the variety show host selection. Under the hierarchy base on four perspectives and 12 criteria, managers of television stations could select the optimal variety show hosts more effectively. The usability and efficiency of the proposed model were also considered by a case study. We offered a distinct contribution to the prior studies by providing a model in the variety show host selection field. In the context of social media competition, this study also added the selection criteria from Internet celebrities. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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23 pages, 1867 KiB  
Article
A Fuzzy Multi-Criteria Analysis of Barriers and Policy Strategies for Small and Medium Enterprises to Adopt Green Innovation
by Almalki Sultan Musaad O, Zhang Zhuo, Almalki Otaibi Musaad O, Zafar Ali Siyal, Hammad Hashmi and Syed Ahsan Ali Shah
Symmetry 2020, 12(1), 116; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12010116 - 07 Jan 2020
Cited by 44 | Viewed by 4310
Abstract
Recently, small and medium enterprises (SMEs) are increasingly focusing on the implementation of green innovation, mainly due to customers’ increasing environmental consciousness. However, SMEs have not yet achieved any significant accomplishment. The lack of success in implementing green practices is due to various [...] Read more.
Recently, small and medium enterprises (SMEs) are increasingly focusing on the implementation of green innovation, mainly due to customers’ increasing environmental consciousness. However, SMEs have not yet achieved any significant accomplishment. The lack of success in implementing green practices is due to various barriers. So, it is crucial to analyze and address these barriers prior to introducing green initiatives. This study prioritizes barriers and solutions to adopt green practices in the context of SMEs in Saudi Arabia. The study develops an integrated decision framework based on symmetry principles to identify main-barriers, sub-barriers, and strategies to overcome these barriers. Six main barriers, 24 sub-barriers, and 10 strategic solutions were identified through literature survey. Then, fuzzy analytical hierarchy process (FAHP) was employed to evaluate main-barriers and sub-barriers. Later, fuzzy technique for order of preference by similarity to ideal solution (FTOPSIS) methodology was used to rank strategies. Results of FAHP revealed that the political barrier category holds higher importance than other barriers. Results of FTOPSIS showed that the strategic solution ‘developing research practices to carryout green innovation in SMEs’ is more important in addressing green innovation barriers in SMEs. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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25 pages, 530 KiB  
Article
Multi-Criteria Group Decision-Making for Selection of Green Suppliers under Bipolar Fuzzy PROMETHEE Process
by Muhammad Akram, Shumaiza and Ahmad N. Al-Kenani
Symmetry 2020, 12(1), 77; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12010077 - 02 Jan 2020
Cited by 48 | Viewed by 3542
Abstract
The preference ranking organization method for enrichment of evaluations (PROMETHEE) method considers a significant outranking class of multi-criteria decision analysis (MCDA), as it is easy to deal with its simple computations. In the PROMETHEE, different preference functions are used according to the type [...] Read more.
The preference ranking organization method for enrichment of evaluations (PROMETHEE) method considers a significant outranking class of multi-criteria decision analysis (MCDA), as it is easy to deal with its simple computations. In the PROMETHEE, different preference functions are used according to the type and nature of attributes or criteria that demonstrate the clearness and reliability of this method. This study provides a new version of the PROMETHEE method using bipolar fuzzy information, named the bipolar fuzzy PROMETHEE method. Bipolar fuzzy sets or numbers constitute an asymmetrical relationship between two judgmental factors of human reasoning. Vague and imprecise knowledge is characterized by bipolar fuzzy linguistic terms which are further represented in the form of trapezoidal bipolar fuzzy numbers. The trapezoidal bipolar fuzzy numbers are used by analysts to assign the preferences of alternatives on the basis of criteria. Further, a ranking function of bipolar fuzzy numbers is considered to access the crisp real preferences of alternatives. The entropy weighting information is employed to calculate the weights of attributes by considering the condition of normality. A numerical example such as the selection of green suppliers by using the bipolar fuzzy PROMETHEE is performed on the basis of the usual criterion preference function in order to explain the procedure of the proposed method. Comparable results are derived by using the combination of linear and level preference functions. The results obtained by using different types of preference functions are the same, representing the authenticity of the proposed bipolar fuzzy PROMETHEE method. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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33 pages, 412 KiB  
Article
Multi-Attribute Decision-Making Based on m-Polar Fuzzy Hamacher Aggregation Operators
by Neha Waseem, Muhammad Akram and José Carlos R. Alcantud
Symmetry 2019, 11(12), 1498; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11121498 - 10 Dec 2019
Cited by 50 | Viewed by 3872
Abstract
In this paper, we introduce certain aggregation operators, namely, the m-polar fuzzy (mF) Hamacher weighted average operator, mF Hamacher ordered weighted average (mFHOWA) operator, mF Hamacher hybrid average (mFHHA) operator, mF Hamacher weighted [...] Read more.
In this paper, we introduce certain aggregation operators, namely, the m-polar fuzzy (mF) Hamacher weighted average operator, mF Hamacher ordered weighted average (mFHOWA) operator, mF Hamacher hybrid average (mFHHA) operator, mF Hamacher weighted geometric (mFHWG) operator, mF Hamacher weighted ordered geometric operator, and mF Hamacher hybrid geometric (mFHHG) operator. We discuss some properties of these operators, inclusive of their ability to implement both symmetric and asymmetric treatments of the items. We develop an algorithmic model to solve multi-attribute decision-making (MADM) problems in mF environment using mF Hamacher weighted average operator (mFHWA) and mFHWG operators. They can compensate for the possible asymmetric roles of the attributes that describe the problem. In the end, to prove the validity and feasibility of the proposed work, we give applications for selecting the most affected country regarding human trafficking, selecting health care waste treatment methods and selecting the best company for investment. We also solve practical MADM problems by using ELECTRE-I method, and give a comparative analysis. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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Review

Jump to: Research

25 pages, 2178 KiB  
Review
Generating Clustering-Based Interval Fuzzy Type-2 Triangular and Trapezoidal Membership Functions: A Structured Literature Review
by Siti Hajar Khairuddin, Mohd Hilmi Hasan, Manzoor Ahmed Hashmani and Muhammad Hamza Azam
Symmetry 2021, 13(2), 239; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13020239 - 31 Jan 2021
Cited by 21 | Viewed by 3384
Abstract
Clustering is more popular than the expert knowledge approach in Interval Fuzzy Type-2 membership function construction because it can construct membership function automatically with less time consumption. Most research proposed a two-fuzzifier fuzzy C-Means clustering method to construct Interval Fuzzy Type-2 membership function [...] Read more.
Clustering is more popular than the expert knowledge approach in Interval Fuzzy Type-2 membership function construction because it can construct membership function automatically with less time consumption. Most research proposed a two-fuzzifier fuzzy C-Means clustering method to construct Interval Fuzzy Type-2 membership function which mainly focused on producing Gaussian membership function. The other two important membership functions, triangular and trapezoidal, are constructed using the grid partitioning method. However, the method suffers a drawback of not being able to represent actual data composition in the underlying dataset. Some research proposed triangular and trapezoidal membership functions construction using readily formed Fuzzy Type-1 membership functions, which means it remains unclear how the membership functions are heuristically constructed using fuzzy C-Means outputs. The triangular and trapezoidal membership functions are important because previous works have shown that they may produce superior performance than Gaussian membership function in some applications. Therefore, this paper presents a structured literature review on generating triangular and trapezoidal Interval Fuzzy Type-2 membership functions using fuzzy C-Means. Initially, 110 related manuscripts were collected from Web of Science, Scopus, and Google Scholar. These manuscripts went through the identification, screening, eligibility, and inclusion processes, and as a result, 21 manuscripts were reviewed and discussed in this paper. To ensure that the review also covers the important components of fuzzy logic, this paper also reviews and discusses another 49 manuscripts on fuzzy calculation and operation. Furthermore, this paper also discusses the contributions of the conducted review to the body of knowledge, future research directions and challenges, with the aim to motivate the future works of constructing the methods to generate Interval Fuzzy Type-2 triangular and trapezoidal membership functions using fuzzy C-Means. The methods imply flexibility in choosing membership function type, hence increasing the effectiveness of fuzzy applications through leveraging the advantages that each of the three membership function types could provide. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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20 pages, 352 KiB  
Review
Some Construction Methods of Aggregation Operators in Decision-Making Problems: An Overview
by Azadeh Zahedi Khameneh and Adem Kilicman
Symmetry 2020, 12(5), 694; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12050694 - 01 May 2020
Cited by 8 | Viewed by 2655
Abstract
Aggregating data is the main line of any discipline dealing with fusion of information from the knowledge-based systems to decision-making. The purpose of aggregation methods is to convert a list of objects, all belonging to a given set, into a single representative object [...] Read more.
Aggregating data is the main line of any discipline dealing with fusion of information from the knowledge-based systems to decision-making. The purpose of aggregation methods is to convert a list of objects, all belonging to a given set, into a single representative object of the same set usually by an n-ary function, so-called aggregation operator. As the useful aggregation functions for modeling real-life problems are limited, the basic problem is to construct a proper aggregation operator, usually a symmetric one, for each situation. During the last decades, a number of construction methods for aggregation functions have been developed to build new classes based on the existing well-known operators. There are three main construction methods in common use: transformation, composition, and convex combination. This paper compares these methods with respect to the type of aggregating problems that can be handled by each of them. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
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