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Symmetry
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Uncertain Multi-Criteria Optimization Problems
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Uncertain Multi-Criteria Optimization Problems

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 97573

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Dr. Dragan Pamucar

grade E-Mail Website
Guest Editor
Department of logistics, University of Defence, Belgrade, Pavla Jurišića Šturma 33, 11000 Belgrade, Serbia
Interests: multi-criteria decision making problems; computational intelligence; sustainability neuro-fuzzy systems; fuzzy; rough and intuitionistic fuzzy set theory; neutrosophic theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relations used when modeling optimization problems. Moreover, the notion of symmetry appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better with respect to one objective may be a compromising one for other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories like probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems are not yet to be explored in-depth and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed on various uncertain frameworks with special emphasis on optimization problems.

This Special Issue on “Uncertain Multi-Criteria Optimization Problems” aims to incorporate recent developments in the area of applied science. Topics include, but are not limited to, the following:

  • Theoretical foundations of MCDM using uncertainty,
  • Aggregation operators and application in MCDM
  • Multi-criteria in production and logistics
  • Risk analysis/modeling, sensitivity/robustness analysis
  • Multi-criteria network optimization
  • Mathematical programming in MCDM under uncertainty
  • New trends in multi-criteria decision-making

Dr. Dragan Pamučar
Guest Editor

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

  • mathematical programming in MCDM
  • fuzzy set theory
  • neutrosophic theory
  • rough set theory
  • grey theory
  • engineering applications

Published Papers (30 papers)

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Research

30 pages, 856 KiB  
Article
Multiple Granulation Rough Set Approach to Interval-Valued Intuitionistic Fuzzy Ordered Information Systems
by Zhen Li and Xiaoyan Zhang
Symmetry 2021, 13(6), 949; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13060949 - 27 May 2021
Cited by 1 | Viewed by 1808
Abstract
As a further extension of the fuzzy set and the intuitive fuzzy set, the interval-valued intuitive fuzzy set (IIFS) is a more effective tool to deal with uncertain problems. However, the classical rough set is based on the equivalence relation, which do not [...] Read more.
As a further extension of the fuzzy set and the intuitive fuzzy set, the interval-valued intuitive fuzzy set (IIFS) is a more effective tool to deal with uncertain problems. However, the classical rough set is based on the equivalence relation, which do not apply to the IIFS. In this paper, we combine the IIFS with the ordered information system to obtain the interval-valued intuitive fuzzy ordered information system (IIFOIS). On this basis, three types of multiple granulation rough set models based on the dominance relation are established to effectively overcome the limitation mentioned above, which belongs to the interdisciplinary subject of information theory in mathematics and pattern recognition. First, for an IIFOIS, we put forward a multiple granulation rough set (MGRS) model from two completely symmetry positions, which are optimistic and pessimistic, respectively. Furthermore, we discuss the approximation representation and a few essential characteristics for the target concept, besides several significant rough measures about two kinds of MGRS symmetry models are discussed. Furthermore, a more general MGRS model named the generalized MGRS (GMGRS) model is proposed in an IIFOIS, and some important properties and rough measures are also investigated. Finally, the relationships and differences between the single granulation rough set and the three types of MGRS are discussed carefully by comparing the rough measures between them in an IIFOIS. In order to better utilize the theory to realistic problems, an actual case shows the methods of MGRS models in an IIFOIS is given in this paper. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
24 pages, 1208 KiB  
Article
Risk Assessment of Circuit Breakers Using Influence Diagrams with Interval Probabilities
by Jelena D. Velimirovic and Aleksandar Janjic
Symmetry 2021, 13(5), 737; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13050737 - 21 Apr 2021
Cited by 5 | Viewed by 2495
Abstract
This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability and decision theory methods. More specifically, influence diagrams—as extended Bayesian network functions with interval probabilities represented through credal sets—were chosen for [...] Read more.
This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability and decision theory methods. More specifically, influence diagrams—as extended Bayesian network functions with interval probabilities represented through credal sets—were chosen for the predictive modelling scenario of replacing the most critical circuit breakers in optimal time. Namely, based on the available data on circuit breakers and other variables that affect the considered model of a complex power system, a group of experts was able to assess the situation using interval probabilities instead of crisp probabilities. Furthermore, the paper examines how the confidence interval width affects decision-making in this context and eliminates the information asymmetry of different experts. Based on the obtained results for each considered interval width separately on the action to be taken over the considered model in order to minimize the risk of the power system failure, it can be concluded that the proposed approach clearly indicates the advantages of using interval probability when making decisions in systems such as the one considered in this paper. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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24 pages, 3063 KiB  
Article
Multi-Criteria Seed Selection for Targeting Multi-Attribute Nodes in Complex Networks
by Artur Karczmarczyk, Jarosław Jankowski and Jarosław Wątrobski
Symmetry 2021, 13(4), 731; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13040731 - 20 Apr 2021
Cited by 3 | Viewed by 2008
Abstract
Online environments have evolved from the early-stage technical systems to social platforms with social communication mechanisms resembling the interactions which can be found in the real world. Online marketers are using the close relations between the users of social networks to more easily [...] Read more.
Online environments have evolved from the early-stage technical systems to social platforms with social communication mechanisms resembling the interactions which can be found in the real world. Online marketers are using the close relations between the users of social networks to more easily propagate the marketing contents in their advertising campaigns. Such viral marketing campaigns have proven to provide better results than traditional online marketing, hence the increasing research interest in the topic. While the majority of the up-to-date research focuses on maximizing the global coverage and influence in the complete network, some studies have been conducted in the area of budget-constrained conditions as well as in the area of targeting particular groups of nodes. In this paper, a novel approach to targeting multi-attribute nodes in complex networks is presented, in which an MCDA method with various preference weights for all criteria is used to select the initial seeds to best reach the targeted nodes in the network. The proposed approach shows some symmetric characteristics—while the global coverage in the network is decreased, the coverage amongst the targeted nodes grows. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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28 pages, 468 KiB  
Article
Cubic M-polar Fuzzy Hybrid Aggregation Operators with Dombi’s T-norm and T-conorm with Application
by Muhammad Riaz, Muhammad Abdullah Khokhar, Dragan Pamucar and Muhammad Aslam
Symmetry 2021, 13(4), 646; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13040646 - 11 Apr 2021
Cited by 6 | Viewed by 1832
Abstract
A cubic m-polar fuzzy set (CmPFS) is a new hybrid extension of cubic set (CS) and m-polar fuzzy set (mPFS). A CS comprises two parts; one part consists of a fuzzy interval (may sometimes be a fuzzy number) acting as membership grade (MG), [...] Read more.
A cubic m-polar fuzzy set (CmPFS) is a new hybrid extension of cubic set (CS) and m-polar fuzzy set (mPFS). A CS comprises two parts; one part consists of a fuzzy interval (may sometimes be a fuzzy number) acting as membership grade (MG), and the second part consists of a fuzzy number acting as non-membership grade (NMG). An mPFS assigns m number of MGs against each alternative in the universe of discourse. A CmPFS deals with single as well as multi-polar information in the cubic environment. In this article, we explore some new aspects and consequences of the CmPFS. We define score and accuracy functions to find the priorities of alternatives/objects in multi-criteria decision-making (MCDM). For this objective, some new operations, like addition, scalar/usual multiplication, and power, are defined under Dombi’s t-norm and t-conorm. We develop several new aggregation operators (AOs) using cubic m-polar fuzzy Dombi’s t-norm and t-conorm. We present certain properties of suggested operators like monotonicity, commutativity, idempotency, and boundedness. Additionally, to discuss the application of these AOs, we present an advanced superiority and inferiority ranking (SIR) technique to deal with the problem of conversion from a linear economy to a circular economy. Moreover, a comparison analysis of proposed methodology with some other existing methods is also given. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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15 pages, 343 KiB  
Article
On the Analytic Hierarchy Process Structure in Group Decision-Making Using Incomplete Fuzzy Information with Applications
by Atiq ur Rehman, Andrii Shekhovtsov, Nighat Rehman, Shahzad Faizi and Wojciech Sałabun
Symmetry 2021, 13(4), 609; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13040609 - 06 Apr 2021
Cited by 31 | Viewed by 2781
Abstract
The multi-criteria decision-making (MCDM) problem has a solution whose quality can be affected by the experts’ inclinations. Under essential conditions, the fuzzy MCDM method can provide more acceptable and efficient outcomes to select the best alternatives. This work consists of a consensus-based technique [...] Read more.
The multi-criteria decision-making (MCDM) problem has a solution whose quality can be affected by the experts’ inclinations. Under essential conditions, the fuzzy MCDM method can provide more acceptable and efficient outcomes to select the best alternatives. This work consists of a consensus-based technique for selecting and evaluating suppliers in an incomplete fuzzy preference relations (IFPRs) environment utilizing TL-transitivity (Lukasiewicz transitivity). The suggested method is developed based on the criteria of the Analytical Hierarchy Process (AHP) Fframework, and the decision matrix is construtced using consistent fuzzy preference relations (FPRs). We use the symmetrical decisional matrix approach. A variety of numerical explanations and an analysis of quantitative results illustrate the suggested methodology’s logic and effectiveness. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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11 pages, 236 KiB  
Article
Representations of a Comparison Measure between Two Fuzzy Sets
by Juin-Han Chen and Hui-Chin Tang
Symmetry 2020, 12(12), 2008; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12122008 - 05 Dec 2020
Viewed by 1199
Abstract
This paper analyzes the representation behaviors of a comparison measure between two compared fuzzy sets. Three types of restrictions on two fuzzy sets are considered in this paper: two disjoint union fuzzy sets, two disjoint fuzzy sets and two general fuzzy sets. Differences [...] Read more.
This paper analyzes the representation behaviors of a comparison measure between two compared fuzzy sets. Three types of restrictions on two fuzzy sets are considered in this paper: two disjoint union fuzzy sets, two disjoint fuzzy sets and two general fuzzy sets. Differences exist among the numbers of possible representations of a comparison measure for the three types of fuzzy sets restrictions. The value of comparison measure is constant for two disjoint union fuzzy sets. There are 49 candidate representations of a comparison measure for two disjoint fuzzy sets, of which 13 candidate representations with one or two terms are obtained. For each candidate representation, a variant of the general axiomatic definition for a comparison measure is presented. Choosing the right candidate representation for a given application, we can easily and efficiently calculate and compare a comparison measure. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
23 pages, 2093 KiB  
Article
A Hybrid MCDM Model to Evaluate and Classify Outsourcing Providers in Manufacturing
by Ching-Fang Liaw, Wan-Chi Jackie Hsu and Huai-Wei Lo
Symmetry 2020, 12(12), 1962; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12121962 - 27 Nov 2020
Cited by 15 | Viewed by 2347
Abstract
It is a common practice for enterprises to use outsourcing strategies to reduce operating costs and improve product competitiveness. Outsourcing providers or operators need to be aware of environmental protection and make products comply with the restrictions of international environmental regulations. Therefore, this [...] Read more.
It is a common practice for enterprises to use outsourcing strategies to reduce operating costs and improve product competitiveness. Outsourcing providers or operators need to be aware of environmental protection and make products comply with the restrictions of international environmental regulations. Therefore, this study proposes a set of multiple criteria decision-making (MCDM) approaches for systematic green outsourcing evaluation. First, a team of experts is established to discuss mutually dependent relationships among criteria, and the decision-making trial and evaluation laboratory (DEMATEL) technique is applied to generate subjective influential weights. Then, a large amount of data from outsourcing providers is collected, and the criteria importance through the intercriteria correlation (CRITIC) method is used to obtain the objective influential weights. Finally, a novel classifiable technique for ordering preference based on similarity to ideal solutions (classifiable TOPSIS) is proposed to integrate the performance of green outsourcing providers and classify them into four levels. The classifiable TOPSIS improves the shortcomings of conventional TOPSIS and establishes a visual rating diagram to help decision-makers to distinguish the performance of outsourcing providers more clearly. Taking a Taiwanese multinational machine tool manufacturer as an example, the performance of outsourcing providers related to manufacturing activities was investigated to demonstrate the effectiveness and applicability of this proposed model. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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19 pages, 337 KiB  
Article
Sustainable Decision Making Using a Consensus Model for Consistent Hesitant Fuzzy Preference Relations—Water Allocation Management Case Study
by Atiq-ur Rehman, Jarosław Wątróbski, Shahzad Faizi, Tabasam Rashid and Małgorzata Tarczyńska-Łuniewska
Symmetry 2020, 12(12), 1957; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12121957 - 26 Nov 2020
Cited by 1 | Viewed by 1562
Abstract
This paper presents an improved consensus-based procedure to handle multi-person decision making (MPDM) using hesitant fuzzy preference relations (HFPRs) which are not in normal format. At the first level, we proposed a ukasiewicz transitivity (TL-transitivity) based scheme to get normalized [...] Read more.
This paper presents an improved consensus-based procedure to handle multi-person decision making (MPDM) using hesitant fuzzy preference relations (HFPRs) which are not in normal format. At the first level, we proposed a ukasiewicz transitivity (TL-transitivity) based scheme to get normalized hesitant fuzzy preference relations (NHFPRs), subject to which, a consensus-based model is established. Then, a transitive closure formula is defined to construct TL-consistent HFPRs and creates symmetrical matrices. Following this, consistency analysis is made to estimate the consistency degrees of the information provided by the decision-makers (DMs), and consequently, to assign the consistency weights to them. The final priority weights vector of DMs is calculated after the combination of consistency weights and predefined priority weights (if any). The consensus process concludes whether the aggregation of data and selection of the best alternative should be originated or not. The enhancement mechanism is indulged in improving the consensus measure among the DMs, after introducing an identifier used to locate the weak positions, in case of the poor consensus reached. In the end, a comparative example reflects the applicability and the efficiency of proposed scheme. The results show that the proposed method can offer useful comprehension into the MPDM process. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
35 pages, 3704 KiB  
Article
A New Approach to Identifying a Multi-Criteria Decision Model Based on Stochastic Optimization Techniques
by Bartłomiej Kizielewicz and Wojciech Sałabun
Symmetry 2020, 12(9), 1551; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091551 - 20 Sep 2020
Cited by 48 | Viewed by 3400
Abstract
Many scientific papers are devoted to solving multi-criteria problems. Researchers solve these problems, usually using methods that find discrete solutions and with the collaboration of domain experts. In both symmetrical and asymmetrical problems, the challenge is when new decision-making variants emerge. Unfortunately, discreet [...] Read more.
Many scientific papers are devoted to solving multi-criteria problems. Researchers solve these problems, usually using methods that find discrete solutions and with the collaboration of domain experts. In both symmetrical and asymmetrical problems, the challenge is when new decision-making variants emerge. Unfortunately, discreet identification of preferences makes it impossible to determine the preferences for new alternatives. In this work, we propose a new approach to identifying a multi-criteria decision model to address this challenge. Our proposal is based on stochastic optimization techniques and the characteristic objects method (COMET). An extensive work comparing the use of hill-climbing, simulated annealing, and particle swarm optimization algorithms are presented in this paper. The paper also contains preliminary studies on initial conditions. Finally, our approach has been demonstrated using a simple numerical example. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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56 pages, 2440 KiB  
Article
Are MCDA Methods Benchmarkable? A Comparative Study of TOPSIS, VIKOR, COPRAS, and PROMETHEE II Methods
by Wojciech Sałabun, Jarosław Wątróbski and Andrii Shekhovtsov
Symmetry 2020, 12(9), 1549; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091549 - 20 Sep 2020
Cited by 245 | Viewed by 8825
Abstract
Multi-Criteria Decision-Analysis (MCDA) methods are successfully applied in different fields and disciplines. However, in many studies, the problem of selecting the proper methods and parameters for the decision problems is raised. The paper undertakes an attempt to benchmark selected Multi-Criteria Decision Analysis (MCDA) [...] Read more.
Multi-Criteria Decision-Analysis (MCDA) methods are successfully applied in different fields and disciplines. However, in many studies, the problem of selecting the proper methods and parameters for the decision problems is raised. The paper undertakes an attempt to benchmark selected Multi-Criteria Decision Analysis (MCDA) methods. To achieve that, a set of feasible MCDA methods was identified. Based on reference literature guidelines, a simulation experiment was planned. The formal foundations of the authors’ approach provide a reference set of MCDA methods ( Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), Complex Proportional Assessment (COPRAS), and PROMETHEE II: Preference Ranking Organization Method for Enrichment of Evaluations) along with their similarity coefficients (Spearman correlation coefficients and WS coefficient). This allowed the generation of a set of models differentiated by the number of attributes and decision variants, as well as similarity research for the obtained rankings sets. As the authors aim to build a complex benchmarking model, additional dimensions were taken into account during the simulation experiments. The aspects of the performed analysis and benchmarking methods include various weighing methods (results obtained using entropy and standard deviation methods) and varied techniques of normalization of MCDA model input data. Comparative analyses showed the detailed influence of values of particular parameters on the final form and a similarity of the final rankings obtained by different MCDA methods. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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17 pages, 944 KiB  
Article
A Distributionally Robust Chance-Constrained Approach for Modeling Demand Uncertainty in Green Port-Hinterland Transportation Network Optimization
by Qian Dai and Jiaqi Yang
Symmetry 2020, 12(9), 1492; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091492 - 10 Sep 2020
Cited by 8 | Viewed by 2239
Abstract
This paper discusses a bi-objective programming of the port-hinterland freight transportation system based on intermodal transportation with the consideration of uncertain transportation demand for green concern. Economic and environmental aspects are integrated in order to obtain green flow distribution solutions for the proposed [...] Read more.
This paper discusses a bi-objective programming of the port-hinterland freight transportation system based on intermodal transportation with the consideration of uncertain transportation demand for green concern. Economic and environmental aspects are integrated in order to obtain green flow distribution solutions for the proposed port-hinterland network. A distributionally robust chance constraint optimization model is then established for the uncertainty of transportation demand, in which the chance constraint is described such that transportation demand is satisfied under the worst-case distribution based on the partial information of the mean and variance. The trade-offs among different objectives and the uncertainty theory applied in the modeling both involve the notion of symmetry. Taking the actual port-hinterland transportation network of the Yangtze River Economic Belt as an example, the results reveal that the railway-road intermodal transport is promoted and the change in total network CO2 emissions is contrary to that in total network costs. Additionally, both network costs and network emissions increase significantly with the growth of the lower bound of probability for chance constraint. The higher the probability level grows, the greater the trade-offs between two objectives are influenced, which indicates that the operation capacity of inland intermodal terminals should be increased to meet the high probability level. These findings can help provide decision supports for the green development strategy of the port-hinterland container transportation network, which meanwhile faces a dynamic planning problem caused by stochastic demands in real life. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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21 pages, 960 KiB  
Article
An Extended Shapley TODIM Approach Using Novel Exponential Fuzzy Divergence Measures for Multi-Criteria Service Quality in Vehicle Insurance Firms
by Arunodaya Raj Mishra, Pratibha Rani, Abbas Mardani, Reetu Kumari, Edmundas Kazimieras Zavadskas and Dilip Kumar Sharma
Symmetry 2020, 12(9), 1452; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091452 - 03 Sep 2020
Cited by 11 | Viewed by 2228
Abstract
Classification of the divergence measure for fuzzy sets (FSs) has been a successful approach since it has been utilized in several disciplines, e.g., image segmentation, pattern recognition, decision making, etc. The objective of the manuscript is to show the advantage of the combined [...] Read more.
Classification of the divergence measure for fuzzy sets (FSs) has been a successful approach since it has been utilized in several disciplines, e.g., image segmentation, pattern recognition, decision making, etc. The objective of the manuscript is to show the advantage of the combined methodology. A comparison clearly shows the usefulness of the proposed technique over the existing ones under the fuzzy environment. This study presents novel exponential-type divergence measures with some elegant features, which can be applied to FSs. Next, a TODIM (an acronym in Portuguese for Interactive Multicriteria Decision Making) approach derived from prospect theory, Shapley function, and divergence measure for multi-criteria decision-making (MCDM) is proposed. Besides, for the reason of evaluating the dominance degree of the option, and the weights of the criteria, proposed divergence measures are implemented. Evaluating and selecting the service quality is the most important issue in management; it has a direct influence on the way the manufacturer performs its tasks. Selecting the service quality can be thought of as a problem of MCDM involving numerous contradictory criteria (whether of a quantitative or qualitative nature) for the evaluation processes. In recent years, the service quality assessment is becoming increasingly complex and uncertain; as a result, some criteria assessment processes cannot be efficiently done by numerical assessments. In addition, decision experts (DEs) may not always show full rationality in different real-life situations that need decision making. Here, a real service quality evaluation problem is considered to discuss the efficacy of the developed methods. The algorithm (TODIM based on the Shapley function and divergence measures) has a unique procedure among MCDM approaches, which is demonstrated for the first time in this paper. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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15 pages, 513 KiB  
Article
Intuitionistic Fuzzy Sets in Multi-Criteria Group Decision Making Problems Using the Characteristic Objects Method
by Shahzad Faizi, Wojciech Sałabun, Tabasam Rashid, Sohail Zafar and Jarosław Wątróbski
Symmetry 2020, 12(9), 1382; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091382 - 19 Aug 2020
Cited by 50 | Viewed by 3605
Abstract
Over the past few decades, several researchers and professionals have focused on the development and application of multi-criteria group decision making (MCGDM) methods under a fuzzy environment in different areas and disciplines. This complex research area has become one of the more popular [...] Read more.
Over the past few decades, several researchers and professionals have focused on the development and application of multi-criteria group decision making (MCGDM) methods under a fuzzy environment in different areas and disciplines. This complex research area has become one of the more popular topics, and it seems that this trend will be increasing. In this paper, we propose a new MCGDM approach combining intuitionistic fuzzy sets (IFSs) and the Characteristic Object Method (COMET) for solving the group decision making (GDM) problems. The COMET method is resistant to the rank reversal phenomenon, and at the same time it remains relatively simple and intuitive in practical problems. This method can be used for both symmetric and asymmetric information. The Triangular Intuitionistic Fuzzy Numbers (TIFNs) have been used to handle uncertain data. This concept can ensure the preference information about an alternative under specific criteria more comprehensively and allows for easy modelling of symmetrical or asymmetrical linguistic values. Each expert provides the membership and non-membership degree values of intuitionistic fuzzy numbers (IFNs). So this approach deals with a different kind of uncertainty than with hesitant fuzzy sets (HFSs). The proposed combination of COMET and IFSs required an adaptation of the matrix of expert judgment (MEJ) and allowed to capture the behaviour aspects of the decision makers (DMs). Therefore, we get more reliable solutions while solving MCGDM problems. Finally, the proposed method is presented in a simple academic example. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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31 pages, 754 KiB  
Article
q-Rung Orthopair Fuzzy Geometric Aggregation Operators Based on Generalized and Group-Generalized Parameters with Application to Water Loss Management
by Muhammad Riaz, Ayesha Razzaq, Humaira Kalsoom, Dragan Pamučar, Hafiz Muhammad Athar Farid and Yu-Ming Chu
Symmetry 2020, 12(8), 1236; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081236 - 27 Jul 2020
Cited by 23 | Viewed by 2222
Abstract
The notions of fuzzy set (FS) and intuitionistic fuzzy set (IFS) make a major contribution to dealing with practical situations in an indeterminate and imprecise framework, but there are some limitations. Pythagorean fuzzy set (PFS) is an extended form of the IFS, in [...] Read more.
The notions of fuzzy set (FS) and intuitionistic fuzzy set (IFS) make a major contribution to dealing with practical situations in an indeterminate and imprecise framework, but there are some limitations. Pythagorean fuzzy set (PFS) is an extended form of the IFS, in which degree of truthness and degree of falsity meet the condition 0≤Θ˘2(x)+K2(x)≤1. Another extension of PFS is a q´-rung orthopair fuzzy set (q´-ROFS), in which truthness degree and falsity degree meet the condition 0≤Θ˘q´(x)+Kq´(x)≤1,(q´≥1), so they can characterize the scope of imprecise information in more comprehensive way. q´-ROFS theory is superior to FS, IFS, and PFS theory with distinguished characteristics. This study develops a few aggregation operators (AOs) for the fusion of q´-ROF information and introduces a new approach to decision-making based on the proposed operators. In the framework of this investigation, the idea of a generalized parameter is integrated into the q´-ROFS theory and different generalized q´-ROF geometric aggregation operators are presented. Subsequently, the AOs are extended to a “group-based generalized parameter”, with the perception of different specialists/decision makers. We developed q´-ROF geometric aggregation operator under generalized parameter and q´-ROF geometric aggregation operator under group-based generalized parameter. Increased water requirements, in parallel with water scarcity, force water utilities in developing countries to follow complex operating techniques for the distribution of the available amounts of water. Reducing water losses from water supply systems can help to bridge the gap between supply and demand. Finally, a decision-making approach based on the proposed operator is being built to solve the problems under the q´-ROF environment. An illustrative example related to water loss management has been given to show the validity of the developed method. Comparison analysis between the proposed and the existing operators have been performed in term of counter-intuitive cases for showing the liability and dominance of proposed techniques to the existing one is also considered. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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39 pages, 917 KiB  
Article
Linear Diophantine Fuzzy Soft Rough Sets for the Selection of Sustainable Material Handling Equipment
by Muhammad Riaz, Masooma Raza Hashmi, Humaira Kalsoom, Dragan Pamucar and Yu-Ming Chu
Symmetry 2020, 12(8), 1215; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081215 - 24 Jul 2020
Cited by 65 | Viewed by 3492
Abstract
The concept of linear Diophantine fuzzy sets (LDFSs) is a new approach for modeling uncertainties in decision analysis. Due to the addition of reference or control parameters with membership and non-membership grades, LDFS is more flexible and reliable than existing concepts of intuitionistic [...] Read more.
The concept of linear Diophantine fuzzy sets (LDFSs) is a new approach for modeling uncertainties in decision analysis. Due to the addition of reference or control parameters with membership and non-membership grades, LDFS is more flexible and reliable than existing concepts of intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy sets (PFSs), and q-rung orthopair fuzzy sets (q-ROFSs). In this paper, the notions of linear Diophantine fuzzy soft rough sets (LDFSRSs) and soft rough linear Diophantine fuzzy sets (SRLDFSs) are proposed as new hybrid models of soft sets, rough sets, and LDFS. The suggested models of LDFSRSs and SRLDFSs are more flexible to discuss fuzziness and roughness in terms of upper and lower approximation operators. Certain operations on LDFSRSs and SRLDFSs have been established to discuss robust multi-criteria decision making (MCDM) for the selection of sustainable material handling equipment. For these objectives, some algorithms are developed for the ranking of feasible alternatives and deriving an optimal decision. Meanwhile, the ideas of the upper reduct, lower reduct, and core set are defined as key factors in the proposed MCDM technique. An application of MCDM is illustrated by a numerical example, and the final ranking in the selection of sustainable material handling equipment is computed by the proposed algorithms. Finally, a comparison analysis is given to justify the feasibility, reliability, and superiority of the proposed models. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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25 pages, 2836 KiB  
Article
Fuzzy Random Chance-Constrained Programming Model for the Vehicle Routing Problem of Hazardous Materials Transportation
by Liying Zhao and Ningbo Cao
Symmetry 2020, 12(8), 1208; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081208 - 23 Jul 2020
Cited by 10 | Viewed by 2101
Abstract
As an indispensable necessity in daily routine of citizens, hazardous materials (Hazmat) not only plays an increasingly important role, but also brings a series of transportation uncertainty phenomena, the most prominent of which is a safety problem. When it attempts to find the [...] Read more.
As an indispensable necessity in daily routine of citizens, hazardous materials (Hazmat) not only plays an increasingly important role, but also brings a series of transportation uncertainty phenomena, the most prominent of which is a safety problem. When it attempts to find the best vehicle route scheme that can possess the lowest risk attribute in a fuzzy random environment for a single warehouse, the influence of cost should also be taken into account. In this study, a new mathematical theory was conducted in the modeling process. To take a full consideration of uncertainty, vehicle travel distance and population density along the road segment were assumed to be fuzzy variables. Meanwhile, accident probability and vehicle speed were set to be stochastic. Furthermore, based on the assumptions, authors established three chance constrained programming models according to the uncertain theory. Model I was used to seek the achievement of minimum risk of the vehicle route scheme, using traditional risk model; the goal of Model II was to obtain the lowest total cost, including the green cost, and the main purpose of Model III was to establish a balance between cost and risk. To settle the above models, a hybrid intelligent algorithm was designed, which was a combination of genetic algorithm and fuzzy random simulation algorithm, which simultaneously proved its convergence. At last, two experiments were designed to illustrate the feasibility of the proposed models and algorithms. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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37 pages, 532 KiB  
Article
A Robust q-Rung Orthopair Fuzzy Einstein Prioritized Aggregation Operators with Application towards MCGDM
by Muhammad Riaz, Hafiz Muhammad Athar Farid, Humaira Kalsoom, Dragan Pamučar and Yu-Ming Chu
Symmetry 2020, 12(6), 1058; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12061058 - 26 Jun 2020
Cited by 46 | Viewed by 2822
Abstract
A q-rung orthopair fuzzy set (q-ROFS) provides a significant mechanism for managing symmetrical aspects in real life circumstances. The renowned distinguishing feature of q-ROFS is that the sum of the qth powers to each membership degree (MD) and non-membership degree (NMD) is less [...] Read more.
A q-rung orthopair fuzzy set (q-ROFS) provides a significant mechanism for managing symmetrical aspects in real life circumstances. The renowned distinguishing feature of q-ROFS is that the sum of the qth powers to each membership degree (MD) and non-membership degree (NMD) is less than or equal 1, and therefore the comprehensive uncertain space for q-ROF information is broader. Numerous researchers have suggested several aggregation operators based on q-ROFSs. In order to discuss prioritized relationship in the criterion and a smooth approximation of q-ROF information, we introduced q-rung orthopair fuzzy Einstein prioritized weighted averaging (q-ROFEPWA) operator and q-rung orthopair fuzzy Einstein prioritized weighted geometric (q-ROFEPWG) operator. Additionally, we presented a multi-criteria group decision making (MCGDM) technique based on q-rung orthopair fuzzy Einstein prioritized aggregation operators. These operators can evaluate the possible symmetric roles of the criterion that express the real phenomena of the problem. In order to investigate characteristic of suggested operators regarding the symmetry of attributes and their symmetrical roles under q-ROF information, we presented an application of Einstein prioritized aggregation operators. Finally, by comparing it with some other established representative MCGDM models, an illustrative example is provided to check the feasibility, efficiency and supremacy of the proposed technique. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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23 pages, 828 KiB  
Article
A Multicriteria Decision Aid-Based Model for Measuring the Efficiency of Business-Friendly Cities
by Mihailo Jovanović, Slobodan Nedeljković, Milan Ranđelović, Gordana Savić, Vladica Stojanović, Vladimir Stojanović and Dragan Ranđelović
Symmetry 2020, 12(6), 1025; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12061025 - 17 Jun 2020
Cited by 5 | Viewed by 2197
Abstract
Local self-government has the task of enabling stable economic development, in addition to enabling a normal quality of life for citizens. This is why the state government should provide guidelines that will improve the local business climate, and by doing so enable local [...] Read more.
Local self-government has the task of enabling stable economic development, in addition to enabling a normal quality of life for citizens. This is why the state government should provide guidelines that will improve the local business climate, and by doing so enable local economic development. This can be done through the introduction of a business-friendly certification procedure, which is influenced by uncertain inputs and influences many output factors. Each local government has the important task of determining its rank of efficiency in this process. A number of methodologies developed to solve this problem are generally divided into two groups: Parametric and non-parametric. These two groups of methodologies could provide quite different results. Therefore, the purpose of this paper was to create a model using both approaches to achieve a balanced symmetrical approach that produces better results than each approach individually. For this purpose, the paper describes a multicriteria decision aid-based model of optimization to evaluate the effectiveness of this process, integrating classification, data envelopment analysis, and stochastic frontier analysis, as well as its application in a case study of business-friendly certification in the Republic of Serbia. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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12 pages, 634 KiB  
Article
Multi-Criteria Decision Model for the Selection of Suppliers in the Textile Industry
by Chia-Nan Wang, Van Tran Hoang Viet, Thanh Phong Ho, Van Thanh Nguyen and Viet Tinh Nguyen
Symmetry 2020, 12(6), 979; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12060979 - 08 Jun 2020
Cited by 32 | Viewed by 5243
Abstract
In recent years, the market of textile and garment materials has been volatile, and the ongoing US-China trade war is creating good opportunities for other markets such as Vietnam, Bangladesh and Mexico to continue to expand their market share in the United States. [...] Read more.
In recent years, the market of textile and garment materials has been volatile, and the ongoing US-China trade war is creating good opportunities for other markets such as Vietnam, Bangladesh and Mexico to continue to expand their market share in the United States. Vietnam is expected to have great advantages thanks to cheap labor cost and strong production capacity. Raw material supplier selection in a volatile competitive environment is crucial for a company to succeed, and supplier selection is a complicate process in which decision-makers must consider multiple quantitative and qualitative features, along with their symmetrical impact, in order to achieve an optimal result. The purpose of selecting the right supplier is to improve competitiveness and product quality, while satisfying customer demand at a minimum production cost. The aim of this paper is to propose a multicriteria decision making model (MCDM) for garment and textile supplier selection. In the first stage, all criteria affecting this process are defined by using the supply chain operations reference model (SCOR) and experts’ opinion. Incorporating hybrid fuzzy set theory into the analytical network process (ANP) model is the most effective tool for addressing complex problems of decision-making, which has a connection with various qualitative criteria; thus, the Fuzzy Analytical Hierarchy Process (FAHP) was applied for determining the weight of all potential suppliers, and the preference ranking organization method for enrichment of evaluations (PROMETHEE II) was used for ranking the supplier. The results of this research will assist researchers and decision makers in identifying, adapting and applying appropriate methods to identify the optimal material suppliers in the textile and garment industry. This research can also be used to support supplier selection decisions in other industries. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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33 pages, 588 KiB  
Article
q-Rung Orthopair Fuzzy Prioritized Aggregation Operators and Their Application Towards Green Supplier Chain Management
by Muhammad Riaz, Dragan Pamucar, Hafiz Muhammad Athar Farid and Masooma Raza Hashmi
Symmetry 2020, 12(6), 976; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12060976 - 08 Jun 2020
Cited by 48 | Viewed by 2695
Abstract
Supply management and environmental concerns are becoming increasingly relevant to scientific decision analysis around the world. Several companies have implemented the green supply chain management (GSCM) approach for attaining economic advantages while retaining sustainable growth for the environment. Green supplier selection has also [...] Read more.
Supply management and environmental concerns are becoming increasingly relevant to scientific decision analysis around the world. Several companies have implemented the green supply chain management (GSCM) approach for attaining economic advantages while retaining sustainable growth for the environment. Green supplier selection has also been analyzed in many literary works as an important part of GSCM, which is considered an important multi-criteria group decision making (MCGDM) problem. The lack of consideration of the relationships of alternatives to the uncertain environment will be the main reason for weak conclusions in some MCGDM problems. To address these drawbacks, we introduce a new approach for selecting green suppliers with the q-rung orthopair fuzzy information, in which the input assessment is considered by using q-rung orthopair fuzzy numbers (q-ROFNs). A q-ROFN is extremely valuable in representing vague information that occurs in these real-world circumstances. The priority relationship of the alternatives to q-rung orthopair fuzzy information is very helpful to deal with GSCM. Consequently, we develop some prioritized operators with q-ROFNs named the q-rung orthopair fuzzy prioritized weighted average (q-ROFPWA) operator and q-rung orthopair fuzzy prioritized weighted geometric (q-ROFPWG) operator. Several important characteristics of these operators such as idempotents, boundary, and monotonicity are also well proven. Finally, an application of the proposed operators is presented for green supplier selection in GSCM. The scientific nature of the proposed methodology is illustrated by a numerical example to validate its rationality, symmetry, and superiority. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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23 pages, 3578 KiB  
Article
An Integrated Multi-Criteria Approach for Planning Railway Passenger Transport in the Case of Uncertainty
by Svetla Stoilova
Symmetry 2020, 12(6), 949; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12060949 - 04 Jun 2020
Cited by 17 | Viewed by 2434
Abstract
The aim of this study is to elaborate on an integrated approach for transport planning in railway passenger transport in the case of uncertainty. The methodology consists of four stages. In the first stage, the parameters of a multi-criteria model in the case [...] Read more.
The aim of this study is to elaborate on an integrated approach for transport planning in railway passenger transport in the case of uncertainty. The methodology consists of four stages. In the first stage, the parameters of a multi-criteria model in the case of uncertainty were determined. This includes defining the criteria for selection of a transport plan; formulation of the alternatives of the transport plan; formulation of the strategies and probability variants of passenger flow variation for each strategy. In the second stage, the weights of the probability variants of the strategies for change in passenger flow were determined using the analytic hierarchy process (AHP) method. The alternatives of the transport plan were ranked by applying the sequential interactive modeling for urban systems (SIMUS) method based on linear programming. The results for the values of the criterion of ranking obtained through the SIMUS method and the weights of the variants of passenger flow variation calculated with the AHP method were used as input in the expected values in the decision tree. The selection of a suitable alternative in the case of uncertainty was conducted in the third stage by applying the decision tree method. In the fourth stage, verification of the results was made using Laplace’s criterion and Hurwitz’s criterion. The integrated multi-criteria approach was applied for Bulgaria’s railway network. The multi-criteria approach elaborated herein could be used for decision-making in the case of uncertainty about passenger flow; to investigate different strategies of passenger flow variation and to make decisions in case of instability of passenger flow or lack of sufficient travel data. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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18 pages, 234 KiB  
Article
Synergies of Text Mining and Multiple Attribute Decision Making: A Criteria Selection and Weighting System in a Prospective MADM Outline
by Sarfaraz Hashemkhani Zolfani and Arman Derakhti
Symmetry 2020, 12(5), 868; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12050868 - 25 May 2020
Cited by 9 | Viewed by 2503
Abstract
In this study, a new way of criteria selection and a weighting system will be presented in a multi-disciplinary framework. Weighting criteria in Multi-Attribute Decision Making (MADM) has been developing as the most attractive section in the field. Although many ideas have been [...] Read more.
In this study, a new way of criteria selection and a weighting system will be presented in a multi-disciplinary framework. Weighting criteria in Multi-Attribute Decision Making (MADM) has been developing as the most attractive section in the field. Although many ideas have been developed during the last decades, there is no such great diversity that can be mentioned in the literature. This study is looking from outside the box and is presenting something totally new by using big data and text mining in a Prospective MADM outline. PMADM is a hybrid interconnected concept between the Futures Studies and MADM fields. Text mining, which is known as a useful tool in Futures Studies, is applied to create a widespread pilot system for weighting and criteria selection in the PMADM outline. Latent Semantic Analysis (LSA), as an influential method inside the general concept of text mining, is applied to show how a data warehouse’s output, which in this case is Scopus, can reach the final criteria selection and weighting of the criteria. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
20 pages, 4526 KiB  
Article
Application of Six Sigma Model on Efficient Use of Vehicle Fleet
by Tatjana Stanivuk, Tamara Gvozdenović, Jelena Žanić Mikuličić and Vesko Lukovac
Symmetry 2020, 12(5), 857; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12050857 - 22 May 2020
Cited by 8 | Viewed by 6283
Abstract
Each business faces large competition in the market, and it is necessary to adopt the most effective methodology as possible in order to obtain the best solution. Six Sigma (6σ) is a set of techniques and tools for process improvement. The tools of [...] Read more.
Each business faces large competition in the market, and it is necessary to adopt the most effective methodology as possible in order to obtain the best solution. Six Sigma (6σ) is a set of techniques and tools for process improvement. The tools of Six Sigma apply within a simple improvement model known as Define–Measure–Analyze–Improve–Control (DMAIC). This paper shows that implementing Six Sigma can be more effective in managing the vehicle fleet. The combination of mathematical, i.e., statistical basis and practice makes Six Sigma so successful. The Six Sigma project, implemented to reduce costs and increase the availability of a vehicle fleet in a selected company, can be widely applied in other similar enterprises. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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20 pages, 6499 KiB  
Article
A New Integrated Fuzzy Approach to Selecting the Best Solution for Business Balance of Passenger Rail Operator: Fuzzy PIPRECIA-Fuzzy EDAS Model
by Slavko Vesković, Željko Stević, Darjan Karabašević, Snježana Rajilić, Sanjin Milinković and Gordan Stojić
Symmetry 2020, 12(5), 743; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12050743 - 05 May 2020
Cited by 30 | Viewed by 2617
Abstract
The analysis of operations of the passenger traffic operator in the Republic of Srpska (RS) showed that the volume of passenger transport has, for the last fifteen years, been in constant decline. It is of particular importance that the operator has, year after [...] Read more.
The analysis of operations of the passenger traffic operator in the Republic of Srpska (RS) showed that the volume of passenger transport has, for the last fifteen years, been in constant decline. It is of particular importance that the operator has, year after year, recorded a negative balance of business. The way out of the current unfavorable situation in the sector of passenger traffic is based on the application of Public Service Obligation (PSO) based on the Regulation 1370/2007. In order to solve the problems, seven realistically possible variants have been identified. This paper defines the criteria for selecting the best variant, as well as a new integrated fuzzy model for the selection of the best variant that will enable the operator to make a profit. To define the weights of criteria in this paper, we have used the fuzzy PIvot Pairwise RElative Criteria Importance Assessment (F-PIPRECIA) method, while for ranking and selection of the best variant, we have used the Fuzzy Evaluation based on Distance from Average Solution (F-EDAS) method. Results show that the seventh variant: “Increase in revenue from ticket sales and PSO services and reduction in costs“ is the best solution in current conditions. Validation tests are performed with different scenarios and approaches and show that the model is stable. A validity test was created consisting of variations in the significance of model input parameters, testing of reverse rank, applying the fuzzy Measurement Alternatives and Ranking according to the COmpromise Solution (F-MARCOS), fuzzy Simple Additive Weighing (F-SAW) method, and fuzzy Technique for Order of Preference by Similarity to Ideal Solution (F-TOPSIS). As a part of the validation tests, Spearman’s coefficient of correlation (SCC) in some scenarios is performed and weights of the criteria have been obtained using the Fuzzy Analytic Hierarchy Process (F-AHP) and Full Consistency Method (FUCOM). Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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23 pages, 4274 KiB  
Article
Robust Multi-Objective Sustainable Reverse Supply Chain Planning: An Application in the Steel Industry
by Jurgita Antucheviciene, Ahmad Jafarnejad, Hannan Amoozad Mahdiraji, Seyed Hossein Razavi Hajiagha and Amir Kargar
Symmetry 2020, 12(4), 594; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12040594 - 08 Apr 2020
Cited by 11 | Viewed by 2865
Abstract
In the design of the supply chain, the use of the returned products and their recycling in the production and consumption network is called reverse logistics. The proposed model aims to optimize the flow of materials in the supply chain network (SCN), and [...] Read more.
In the design of the supply chain, the use of the returned products and their recycling in the production and consumption network is called reverse logistics. The proposed model aims to optimize the flow of materials in the supply chain network (SCN), and determine the amount and location of facilities and the planning of transportation in conditions of demand uncertainty. Thus, maximizing the total profit of operation, minimizing adverse environmental effects, and maximizing customer and supplier service levels have been considered as the main objectives. Accordingly, finding symmetry (balance) among the profit of operation, the environmental effects and customer and supplier service levels is considered in this research. To deal with the uncertainty of the model, scenario-based robust planning is employed alongside a meta-heuristic algorithm (NSGA-II) to solve the model with actual data from a case study of the steel industry in Iran. The results obtained from the model, solving and validating, compared with actual data indicated that the model could optimize the objectives seamlessly and determine the amount and location of the necessary facilities for the steel industry more appropriately. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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19 pages, 1017 KiB  
Article
Using Data Envelopment Analysis and Multi-Criteria Decision-Making Methods to Evaluate Teacher Performance in Higher Education
by Milena Popović, Gordana Savić, Marija Kuzmanović and Milan Martić
Symmetry 2020, 12(4), 563; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12040563 - 05 Apr 2020
Cited by 23 | Viewed by 4888
Abstract
This paper proposes an approach that combines data envelopment analysis (DEA) with the analytic hierarchy process (AHP) and conjoint analysis, as multi-criteria decision-making methods to evaluate teachers’ performance in higher education. This process of evaluation is complex as it involves consideration of both [...] Read more.
This paper proposes an approach that combines data envelopment analysis (DEA) with the analytic hierarchy process (AHP) and conjoint analysis, as multi-criteria decision-making methods to evaluate teachers’ performance in higher education. This process of evaluation is complex as it involves consideration of both objective and subjective efficiency assessments. The efficiency evaluation in the presence of multiple different criteria is done by DEA and results heavily depend on their selection, values, and the weights assigned to them. Objective efficiency evaluation is data-driven, while the subjective efficiency relies on values of subjective criteria usually captured throughout the survey. The conjoint analysis helps with the selection and determining the relative importance of such criteria, based on stakeholder preferences, obtained as an evaluation of experimentally designed hypothetical profiles. An efficient experimental design can be either symmetric or asymmetric depending on the structure of criteria covered by the study. Obtained importance might be a guideline for selecting adequate input and output criteria in the DEA model when assessing teachers’ subjective efficiency. Another reason to use conjoint preferences is to set a basis for weight restrictions in DEA and consequently to increase its discrimination power. Finally, the overall teacher’s efficiency is an AHP aggregation of subjective and objective teaching and research efficiency scores. Given the growing competition in the field of education, a higher level of responsibility and commitment is expected, and it is therefore helpful to identify weaknesses so that they can be addressed. Therefore, the evaluation of teachers’ efficiency at the University of Belgrade, Faculty of Organizational Sciences illustrates the usage of the proposed approach. As results, relatively efficient and inefficient teachers were identified, the reasons and aspects of their inefficiency were discovered, and rankings were made. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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27 pages, 1405 KiB  
Article
Implementing a Novel Use of Multicriteria Decision Analysis to Select IIoT Platforms for Smart Manufacturing
by Roberto Contreras-Masse, Alberto Ochoa-Zezzatti, Vicente García, Luis Pérez-Dominguez and Mayra Elizondo-Cortés
Symmetry 2020, 12(3), 368; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12030368 - 02 Mar 2020
Cited by 26 | Viewed by 3733
Abstract
Industry 4.0 is having a great impact in all smart efforts. This is not a single product but is composed of several technologies, one of them being Industrial Internet of Things (IIoT). Currently, there are very varied implementation options offered by several companies, [...] Read more.
Industry 4.0 is having a great impact in all smart efforts. This is not a single product but is composed of several technologies, one of them being Industrial Internet of Things (IIoT). Currently, there are very varied implementation options offered by several companies, and this imposes a new challenge to companies that want to implement IIoT in their processes. This challenge suggests using multi-criteria analysis to make a repeatable and justified decision, requiring a set of alternatives and criteria. This paper proposes a new methodology and comprehensive criteria to help organizations to take an educated decision by applying multi-criteria analysis. Here, we suggest a new original use of PROMETHEE-II with a full example from weight calculation up to IIoT platform selection, showing this methodology as an effective study for other organizations interested in selecting an IIoT platform. The criteria proposed stands out from previous work by including not only technical aspects, but economic and social criteria, providing a full view of the problem analyzed. A case of study was used to prove this proposed methodology and finds the minimum subset to reach the best possible ranking. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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26 pages, 2025 KiB  
Article
Assessing Factors for Designing a Successful B2C E-Commerce Website Using Fuzzy AHP and TOPSIS-Grey Methodology
by Ran Li and Tao Sun
Symmetry 2020, 12(3), 363; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12030363 - 02 Mar 2020
Cited by 25 | Viewed by 5804
Abstract
The recent hype in online purchasing has skyrocketed the importance of the electronic commerce (e-commerce) industry. One of the core segments of this industry is business-to-consumer (B2C) where businesses use their websites to sell products and services directly to consumers. Thus, it must [...] Read more.
The recent hype in online purchasing has skyrocketed the importance of the electronic commerce (e-commerce) industry. One of the core segments of this industry is business-to-consumer (B2C) where businesses use their websites to sell products and services directly to consumers. Thus, it must be taken care of that B2C websites are designed in a way which can build a trustworthy and long-term relationship between businesses and consumers. Thus, this study assesses and prioritizes factors for designing a successful B2C e-commerce website. The study employs multi-criteria decision making (MCDM), and to minimize any ambiguity and greyness in the decision-making, it integrates fuzzy and grey respectively with the Analytical Hierarchy Process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to form FAHP and TOPSIS-Grey. Initially, the study conducts a thorough literature survey to screen important factors reported in past studies. Five main factors and nineteen sub-factors were selected for further prioritization. Later, FAHP prioritized factors based on their importance. Finally, based on the FAHP results, TOPSIS-Grey ranked five alternatives (e-commerce websites). FAHP revealed “service quality” as the most successful website designing factor, while TOPSIS-Grey reported “Website-3” as the most successful website, having incorporated the factors required to design a successful website. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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21 pages, 1525 KiB  
Article
Integrated Decision-Making Approach Based on SWARA and GRA Methods for the Prioritization of Failures in Solar Panel Systems under Z-Information
by Saeid Jafarzadeh Ghoushchi, Mohd Nizam Ab Rahman, Diba Raeisi, Elnaz Osgooei and Majid Jafarzadeh Ghoushji
Symmetry 2020, 12(2), 310; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12020310 - 21 Feb 2020
Cited by 26 | Viewed by 3577
Abstract
Encountering a problem or error in the final stages of providing products or services increases costs and delays scheduling. The key task is to ensure quality and reliability in the early stages of the production process and prevent errors from occurring from the [...] Read more.
Encountering a problem or error in the final stages of providing products or services increases costs and delays scheduling. The key task is to ensure quality and reliability in the early stages of the production process and prevent errors from occurring from the beginning. Failure mode and effect analysis (FMEA) is one of the tools for identifying potential problems and their impact on products and services. The conventional FMEA technique has been criticized extensively due to its disadvantages. In this study, the concepts of uncertainty and reliability are considered simultaneously. The processes of weighting risk factors, prioritizing failures by using the stepwise weight assessment ratio analysis (SWARA)–gray relational analysis (GRA) integrated method based on Ζ-number theory and complete prioritization of failures are implemented. Crucial management indices, such as cost and time, are considered in addition to severity, occurrence and detection factors along with assigning symmetric form of the weights to them. This, in turn, increases the interpretability of results and reduces the decision-maker’s subjectivity in risk prioritization. The developed model is implemented on solar panel data with 19 failure modes determined by the FMEA team. Results show that the proposed approach provides a more complete and realistic prioritization of failures than conventional FMEA and fuzzy GRA methods do. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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20 pages, 1496 KiB  
Article
Application of Fuzzy Analytic Hierarchy Process to Underground Mining Method Selection
by Sanja Bajić, Dragoljub Bajić, Branko Gluščević and Vesna Ristić Vakanjac
Symmetry 2020, 12(2), 192; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12020192 - 23 Jan 2020
Cited by 22 | Viewed by 3683
Abstract
The paper proposes a problem-solving approach in the area of underground mining, related to the evaluation and selection of the optimal mining method, employing fuzzy multiple-criteria optimization. The application of fuzzy logic to decision-making in multiple-criteria optimization is particularly useful in cases where [...] Read more.
The paper proposes a problem-solving approach in the area of underground mining, related to the evaluation and selection of the optimal mining method, employing fuzzy multiple-criteria optimization. The application of fuzzy logic to decision-making in multiple-criteria optimization is particularly useful in cases where not enough information is available about a given system, and where expert knowledge and experience are an important aspect. With a straightforward objective, multiple-criteria decision-making is used to rank various mining methods relative to a set of criteria and to select the optimal solution. The considered mining methods represent possible alternatives. In addition, various criteria and subcriteria that influence the selection of the best available solution are defined and analyzed. The final decision concerning the selection of the optimal mining method is made based on mathematical optimization calculations. The paper demonstrates the proposed approach as applied in a case study. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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