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# Special Issue "Entropy Method for Decision Making"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: 15 March 2022.

## Special Issue Editor

Prof. Dr. Pavel Sevastjanov
E-Mail Website
Guest Editor
Department of Computer Science, Częstochowa University of Technology, 42-201 Częstochowa, Poland
Interests: MCDM and optimization in interval and fuzzy settings; MCDM in an interval valued fuzzy setting; MCDM in the type 2 fuzzy setting; MCDM in an intuitionistic fuzzy setting; MCDM based on the synthesis of fuzzy logic and DST; MCDN based on the synthesis of fuzzy logic; intuitionistic fuzzy sets and DST; development of new methods for modern types of uncertainty processing; applications of MCDM in finance and medical diagnostics

## Special Issue Information

Dear Colleagues,

It is well known that any nontrivial decision is burdened with risk. The source of risk is usually a lack of reliable information, in other words, an uncertainty. When making a decision, we usually try to find a compromise between competing criteria of profit (in wide sense) maximization and risk minimization. Thus, some measure of uncertainty is explicitly or implicitly part of decision making. It is important to note that in the most decision making techniques, the criterion of uncertainty minimization is used, but implicitly, without strict mathematical formalization. Although such methods usually provide good results, it seems to be more justified from a methodological point of view to use formalized measures of uncertainty, especially entropy, which plays a key role in the theory of information and has already been successfully used in decision making. Entropy was originally intended to operate with probabilistic uncertainty, but today, in decision making, we deal with a wide spectrum of uncertainties: interval, fuzzy, type 2 fuzzy, interval-valued fuzzy, intuitionistic fuzzy, hesitant fuzzy, evidential (Dempster–Shafer theory of evidence), etc. and their different combinations. In some cases, the basic definition of entropy is adapted to process such types of uncertainty, but generally, there are many new challenges in this field. Therefore, in this Special Issue, we shall encourage the submission of papers devoted to the adaptation of entropy to the solution of multiple criteria decision making (MCDM) problems in the presence of modern types of uncertainty. However, interesting and valuable papers where the problem of uncertainty minimization in MCDM is presented implicitly will be considered as well.

Prof. Dr. Pavel Sevastjanov
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 papers will be 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. Entropy 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 1800 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

• MCDM and entropy in a probabilistic environment
• MCDM and entropy in a possibilistic setting
• MCDM optimization and entropy in interval and fuzzy settings
• MCDM and entropy in an interval valued fuzzy setting
• MCDM and entropy in a type 2 fuzzy setting
• MCDM in an intuitionistic fuzzy setting
• MCDM and entropy based on the synthesis of fuzzy logic and DST
• MCDN and entropy based on the synthesis of fuzzy logic
• intuitionistic fuzzy sets and DST
• development of new methods for modern types of uncertainty processing
• applications of MCDM and entropy in different fields

## Published Papers (12 papers)

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# Research

Article
Entropy Method of Road Safety Management: Case Study of the Russian Federation
Entropy 2022, 24(2), 177; https://0-doi-org.brum.beds.ac.uk/10.3390/e24020177 - 25 Jan 2022
Viewed by 139
Abstract
Within the framework of this paper, the author’s entropy method of road safety management in large-sized systems is considered. The road safety management system in the Russian Federation, the largest country in the world, was selected for this case study. The purpose of [...] Read more.
(This article belongs to the Special Issue Entropy Method for Decision Making)
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Article
A Hybrid Multi-Criteria Decision-Making Approach Based on ANP-Entropy TOPSIS for Building Materials Supplier Selection
Entropy 2021, 23(12), 1597; https://0-doi-org.brum.beds.ac.uk/10.3390/e23121597 - 28 Nov 2021
Cited by 1 | Viewed by 371
Abstract
This article will tell you how to combine “entropy” in the model to reduce the bias of multi-criteria evaluation. Subjective weights are usually determined by decision makers based on their professional background, experience and knowledge, and other factors. The objective weight is obtained [...] Read more.
This article will tell you how to combine “entropy” in the model to reduce the bias of multi-criteria evaluation. Subjective weights are usually determined by decision makers based on their professional background, experience and knowledge, and other factors. The objective weight is obtained by constructing an evaluation matrix of the information based on the actual information of the evaluation criteria of the scheme, and obtained through multi-step calculations. Different decision-making methods are based on different weight types. Considering only one of the two weights often leads to biased results. In addition, in order to establish an effective supply chain, buyers must find suitable merchants among suppliers that provide quality products and/or services. Based on the above factors, it is difficult to choose a suitable alternative. The main contribution of this paper is to combine analytic network process (ANP), entropy weight and the technique for order preference by similarity to an ideal solution (TOPSIS) to construct a suitable multi-criteria decision (MCDM) model. By means of ANP-entropy weights to extend the TOPSIS method, ANP-entropy weights are used to replace subjective weights. A supplier selection decision-making model based on ANP-entropy TOPSIS is proposed. At last, the sensitivity analysis shows that, taking the selection of building materials suppliers as an example, the hybrid ANP-entropy TOPSIS method can effectively select suitable suppliers. Full article
(This article belongs to the Special Issue Entropy Method for Decision Making)
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Article
On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss
Entropy 2021, 23(11), 1485; https://0-doi-org.brum.beds.ac.uk/10.3390/e23111485 - 10 Nov 2021
Viewed by 343
Abstract
In this short paper, a critical analysis of the Neutrosophic, Pythagorean and some other novel fuzzy sets theories foundations is provided, taking into account that they actively used for the solution of the decision-making problems. The shortcomings of these theories are exposed. It [...] Read more.
In this short paper, a critical analysis of the Neutrosophic, Pythagorean and some other novel fuzzy sets theories foundations is provided, taking into account that they actively used for the solution of the decision-making problems. The shortcomings of these theories are exposed. It is stated that the independence hypothesis, which is a cornerstone of the Neutrosophic sets theory, is not in line with common sense and therefore leads to the paradoxical results in the asymptotic limits of this theory. It is shown that the Pythagorean sets theory possesses questionable foundations, the sense of which cannot be explained reasonably. Moreover, this theory does not completely solve the declared problem. Similarly, important methodological problems of other analyzed theories are revealed. To solve the interior problems of the Atanassov’s intuitionistic fuzzy sets and to improve upon them, this being the reason most of the criticized novel sets theories were developed, an alternative approach based on extension of the intuitionistic fuzzy sets in the framework of the Dempster–Shafer theory is proposed. No propositions concerned with the improvement of the Cubic sets theory and Single-Valued Neutrosophic Offset theory were made, as their applicability was shown to be very dubious. In order to stimulate discussion, many statements are deliberately formulated in a hardline form. Full article
(This article belongs to the Special Issue Entropy Method for Decision Making)
Article
Entropy Method for Decision-Making: Uncertainty Cycles in Tourism Demand
Entropy 2021, 23(11), 1370; https://0-doi-org.brum.beds.ac.uk/10.3390/e23111370 - 20 Oct 2021
Viewed by 511
Abstract
A new methodology is presented for measuring, classifying and predicting the cycles of uncertainty that occur in temporary decision-making in the tourist accommodation market (apartments and hotels). Special attention is paid to the role of entropy and cycles in the process under the [...] Read more.
A new methodology is presented for measuring, classifying and predicting the cycles of uncertainty that occur in temporary decision-making in the tourist accommodation market (apartments and hotels). Special attention is paid to the role of entropy and cycles in the process under the Adaptive Markets Hypothesis. The work scheme analyses random cycles from time to time, and in the frequency domain, the linear and nonlinear causality relationships between variables are studied. The period analysed is from January 2005 to December 2018; the following empirical results stand out: (1) On longer scales, the periodicity of the uncertainty of decision-making is between 6 and 12 months, respectively, for all the nationalities described. (2) The elasticity of demand for tourist apartments is approximately 1% due to changes in demand for tourist hotels. (3) The elasticity of the uncertainty factor is highly correlated with the country of origin of tourists visiting Spain. For example, it has been empirically shown that increases of 1% in uncertainty cause increases in the demand for apartments of 2.12% (worldwide), 3.05% (UK), 1.91% (Germany), 1.78% (France), 7.21% (Ireland), 3.61% (The Netherlands) respectively. This modelling has an explanatory capacity of 99% in all the models analysed. Full article
(This article belongs to the Special Issue Entropy Method for Decision Making)
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Article
Intuitionistic Fuzzy TOPSIS as a Method for Assessing Socioeconomic Phenomena on the Basis of Survey Data
Entropy 2021, 23(5), 563; https://0-doi-org.brum.beds.ac.uk/10.3390/e23050563 - 01 May 2021
Cited by 5 | Viewed by 603
Abstract
In the assessment of most complex socioeconomic phenomena with the use of multicriteria methods, continuous data are used, the source of which are most often public statistics. However, there are complex phenomena such as quality of life and quality of services in the [...] Read more.
In the assessment of most complex socioeconomic phenomena with the use of multicriteria methods, continuous data are used, the source of which are most often public statistics. However, there are complex phenomena such as quality of life and quality of services in the assessment, for which questionnaire surveys and ordinal measurement scales are used. In this case, the use of classic multicriteria methods is very difficult, taking into account the way of presenting this type of data by official statistics, as well as their permissible transformations and arithmetic operations. Therefore, the main purpose of this study was the presentation of a novel framework which can be applied for assessing socioeconomic phenomena on the basis of survey data. It was assumed that the object assessments may contain positive or negative opinions and an element of uncertainty expressed in the form a “no”, “difficult to say”, or “no opinion” answers. For this reason, the intuitionistic fuzzy TOPSIS (IF-TOPSIS) method is proposed. To demonstrate the potential of this solution, the results of measuring the subjective quality of life of the inhabitants of 83 cities in EU countries, EFTA countries, the UK, the Western Balkans, and Turkey are presented. For most cities, a high level of subjective quality of life was observed using the proposed approach. The highest level of quality of life was observed in Zurich, whereas the lowest was observed in Palermo. Full article
(This article belongs to the Special Issue Entropy Method for Decision Making)
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Article
Fuzzy Entropy-Based Spatial Hotspot Reliability
Entropy 2021, 23(5), 531; https://0-doi-org.brum.beds.ac.uk/10.3390/e23050531 - 26 Apr 2021
Viewed by 497
Abstract
Cluster techniques are used in hotspot spatial analysis to detect hotspots as areas on the map; an extension of the Fuzzy C-means that the clustering algorithm has been applied to locate hotspots on the map as circular areas; it represents a good trade-off [...] Read more.
Cluster techniques are used in hotspot spatial analysis to detect hotspots as areas on the map; an extension of the Fuzzy C-means that the clustering algorithm has been applied to locate hotspots on the map as circular areas; it represents a good trade-off between the accuracy in the detection of the hotspot shape and the computational complexity. However, this method does not measure the reliability of the detected hotspots and therefore does not allow us to evaluate how reliable the identification of a hotspot of a circular area corresponding to the detected cluster is; a measure of the reliability of hotspots is crucial for the decision maker to assess the need for action on the area circumscribed by the hotspots. We propose a method based on the use of De Luca and Termini’s Fuzzy Entropy that uses this extension of the Fuzzy C-means algorithm and measures the reliability of detected hotspots. We test our method in a disease analysis problem in which hotspots corresponding to areas where most oto-laryngo-pharyngeal patients reside, within a geographical area constituted by the province of Naples, Italy, are detected as circular areas. The results show a dependency between the reliability and fluctuation of the values of the degrees of belonging to the hotspots. Full article
(This article belongs to the Special Issue Entropy Method for Decision Making)
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Article
Performance of Portfolios Based on the Expected Utility-Entropy Fund Rating Approach
Entropy 2021, 23(4), 481; https://0-doi-org.brum.beds.ac.uk/10.3390/e23040481 - 18 Apr 2021
Viewed by 633
Abstract
Yang and Qiu proposed and reframed an expected utility–entropy (EU-E) based decision model. Later on, a similar numerical representation for a risky choice was axiomatically developed by Luce et al. under the condition of segregation. Recently, we established a fund rating approach based [...] Read more.
Yang and Qiu proposed and reframed an expected utility–entropy (EU-E) based decision model. Later on, a similar numerical representation for a risky choice was axiomatically developed by Luce et al. under the condition of segregation. Recently, we established a fund rating approach based on the EU-E decision model and Morningstar ratings. In this paper, we apply the approach to US mutual funds and construct portfolios using the best rating funds. Furthermore, we evaluate the performance of the fund ratings based on the EU-E decision model against Morningstar ratings by examining the performance of the three models in portfolio selection. The conclusions show that portfolios constructed using the ratings based on the EU-E models with moderate tradeoff coefficients perform better than those constructed using Morningstar. The conclusion is robust to different rebalancing intervals. Full article
(This article belongs to the Special Issue Entropy Method for Decision Making)
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Article
A Decision Support Model for Hotel Recommendation Based on the Online Consumer Reviews Using Logarithmic Spherical Hesitant Fuzzy Information
Entropy 2021, 23(4), 432; https://0-doi-org.brum.beds.ac.uk/10.3390/e23040432 - 06 Apr 2021
Cited by 3 | Viewed by 714
Abstract
Spherical hesitant fuzzy sets have recently become more popular in various fields. It was proposed as a generalization of picture hesitant fuzzy sets and Pythagorean hesitant fuzzy sets in order to deal with uncertainty and fuzziness information. Technique of Aggregation is one of [...] Read more.
Spherical hesitant fuzzy sets have recently become more popular in various fields. It was proposed as a generalization of picture hesitant fuzzy sets and Pythagorean hesitant fuzzy sets in order to deal with uncertainty and fuzziness information. Technique of Aggregation is one of the beneficial tools to aggregate the information. It has many crucial application areas such as decision-making, data mining, medical diagnosis, and pattern recognition. Keeping in view the importance of logarithmic function and aggregation operators, we proposed a novel algorithm to tackle the multi-attribute decision-making (MADM) problems. First, novel logarithmic operational laws are developed based on the logarithmic, t-norm, and t-conorm functions. Using these operational laws, we developed a list of logarithmic spherical hesitant fuzzy weighted averaging/geometric aggregation operators to aggregate the spherical hesitant fuzzy information. Furthermore, we developed the spherical hesitant fuzzy entropy to determine the unknown attribute weight information. Finally, the design principles for the spherical hesitant fuzzy decision-making have been developed, and a practical case study of hotel recommendation based on the online consumer reviews has been taken to illustrate the validity and superiority of presented approach. Besides this, a validity test is conducted to reveal the advantages and effectiveness of developed approach. Results indicate that the proposed method is suitable and effective for the decision process to evaluate their best alternative. Full article
(This article belongs to the Special Issue Entropy Method for Decision Making)
Article
A Fuzzy Multiple Criteria Decision Making Approach with a Complete User Friendly Computer Implementation
Entropy 2021, 23(2), 203; https://0-doi-org.brum.beds.ac.uk/10.3390/e23020203 - 07 Feb 2021
Cited by 5 | Viewed by 659
Abstract
The paper presents the generalization of the almost forty years of experience in the field of setting and solving the multiple criteria decision-making (MCDM) problems in various branches of a human activity under different types of uncertainties that inevitably accompany such problems. Based [...] Read more.
The paper presents the generalization of the almost forty years of experience in the field of setting and solving the multiple criteria decision-making (MCDM) problems in various branches of a human activity under different types of uncertainties that inevitably accompany such problems. Based only on the pragmatic intentions, the authors avoid the detailed descriptions of the known methods for the decision-making, while instead focusing on the most frequently used mathematical tools and methodologies in the decision-making practice. Therefore, the paper may be classified as a special kind of illustrative review of the mathematical tools that are focused on applications and are the most used in the solutions of MCDM problems. As an illustrative example, a complete user-friendly computer implementation of such tools and methodology is presented with application to the simple “buying a cat” problem, which, however, possesses all the attributes of the hierarchical fuzzy MCDM task. Full article
(This article belongs to the Special Issue Entropy Method for Decision Making)
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Article
Decision Tree Integration Using Dynamic Regions of Competence
Entropy 2020, 22(10), 1129; https://0-doi-org.brum.beds.ac.uk/10.3390/e22101129 - 05 Oct 2020
Viewed by 881
Abstract
A vital aspect of the Multiple Classifier Systems construction process is the base model integration. For example, the Random Forest approach used the majority voting rule to fuse the base classifiers obtained by bagging the training dataset. In this paper we propose the [...] Read more.
A vital aspect of the Multiple Classifier Systems construction process is the base model integration. For example, the Random Forest approach used the majority voting rule to fuse the base classifiers obtained by bagging the training dataset. In this paper we propose the algorithm that uses partitioning the feature space whose split is determined by the decision rules of each decision tree node which is the base classification model. After dividing the feature space, the centroid of each new subspace is determined. This centroids are used in order to determine the weights needed in the integration phase based on the weighted majority voting rule. The proposal was compared with other Multiple Classifier Systems approaches. The experiments regarding multiple open-source benchmarking datasets demonstrate the effectiveness of our method. To discuss the results of our experiments, we use micro and macro-average classification performance measures. Full article
(This article belongs to the Special Issue Entropy Method for Decision Making)
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Article
Estimating Postural Stability Using Improved Permutation Entropy via TUG Accelerometer Data for Community-Dwelling Elderly People
Entropy 2020, 22(10), 1097; https://0-doi-org.brum.beds.ac.uk/10.3390/e22101097 - 29 Sep 2020
Cited by 5 | Viewed by 889
Abstract
To develop an effective fall prevention program, clinicians must first identify the elderly people at risk of falling and then take the most appropriate interventions to reduce or eliminate preventable falls. Employing feature selection to establish effective decision making can thus assist in [...] Read more.
To develop an effective fall prevention program, clinicians must first identify the elderly people at risk of falling and then take the most appropriate interventions to reduce or eliminate preventable falls. Employing feature selection to establish effective decision making can thus assist in the identification of a patient’s fall risk from limited data. This work therefore aims to supplement professional timed up and go assessment methods using sensor technology, entropy analysis, and statistical analysis. The results showed the different approach of applying logistic regression analysis to the inertial data on a fall-risk scale to allow medical practitioners to predict for high-risk patients. Logistic regression was also used to automatically select feature values and clinical judgment methods to explore the differences in decision making. We also calculate the area under the receiver-operating characteristic curve (AUC). Results indicated that permutation entropy and statistical features provided the best AUC values (all above 0.9), and false positives were avoided. Additionally, the weighted-permutation entropy/statistical features test has a relatively good agreement rate with the short-form Berg balance scale when classifying patients as being at risk. Therefore, the proposed methodology can provide decision-makers with a more accurate way to classify fall risk in elderly people. Full article
(This article belongs to the Special Issue Entropy Method for Decision Making)
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Article
Option Portfolio Selection with Generalized Entropic Portfolio Optimization
Entropy 2020, 22(8), 805; https://0-doi-org.brum.beds.ac.uk/10.3390/e22080805 - 22 Jul 2020
Cited by 1 | Viewed by 1931
Abstract
In this third and final paper of our series on the topic of portfolio optimization, we introduce a further generalized portfolio selection method called generalized entropic portfolio optimization (GEPO). GEPO extends discrete entropic portfolio optimization (DEPO) to include intervals of continuous returns, with [...] Read more.
In this third and final paper of our series on the topic of portfolio optimization, we introduce a further generalized portfolio selection method called generalized entropic portfolio optimization (GEPO). GEPO extends discrete entropic portfolio optimization (DEPO) to include intervals of continuous returns, with direct application to a wide range of option strategies. This lays the groundwork for an adaptable optimization framework that can accommodate a wealth of option portfolios, including popular strategies such as covered calls, married puts, credit spreads, straddles, strangles, butterfly spreads, and even iron condors. These option strategies exhibit mixed returns: a combination of discrete and continuous returns with performance best measured by portfolio growth rate, making entropic portfolio optimization an ideal method for option portfolio selection. GEPO provides the mathematical tools to select efficient option portfolios based on their growth rate and relative entropy. We provide an example of GEPO applied to real market option portfolio selection and demonstrate how GEPO outperforms traditional Kelly criterion strategies. Full article
(This article belongs to the Special Issue Entropy Method for Decision Making)
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