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Entropy Methods for Multicriteria Decision Making

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Multidisciplinary Applications".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 9474

Special Issue Editor


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Guest Editor
Military Academy, University of Defence in Belgrade, Pavla Jurišića Šturma 33, Belgrade 11000, Serbia
Interests: multicriteria decision-making problems; neuro-fuzzy systems; fuzzy, rough, and intuitionistic fuzzy set theory; neutrosophic theory
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Special Issue Information

Dear Colleagues,

The field of multi-criteria decision making (MCDM) began its rapid development in the 1970s. Many methods and their modifications have been developed to improve decision-making processes. The development of rich decision-making tools is accompanied by the fact that MCDM has taken an important place in many scientific fields. With the development of newer methods, the old methods were not forgotten but rather improved following the development of science, and were often used in their original form.

One of the first divisions of MCDM methods is related to objective and subjective decision-support methods. Although subjective methods are more prevalent in scientific research, objective methods have their continuity of application. One of the first objective methods is the entropy method. A simple mathematical apparatus which follows this method ensures the direct generation of criterion weight values based on the mutual contrast of the individual criterion values of the variants for each criterion. In addition to applying it in its standard form, researchers often make various modifications to this method, adapting it to solve different research problems. The most common alterations of the entropy method and others are related to attempts to reduce uncertainty, which is a ubiquitous companion of the decision-making process. For this purpose, MCDM methods are modified by applying mathematical tools that consider uncertainties differently, such as fuzzy sets, rough sets, gray sets, neutrosophic sets, Dempster–Shafer theory, etc. This approach indicates that the development and application of the entropy method have not stopped, but researchers are facing new challenges. In this context, the basic idea of this Special Issue is to collect works dealing with developing the entropy method and its application in solving specific problems. In addition, the Special Issue will also discuss papers that show the application of other objective MCDM methods (i.e., papers that aim to reduce the degree of uncertainty in decision-making processes). Topics include, but are not limited to, the following:

  • Entropy method and MCDM in different fields;
  • Modification of entropy method using fuzzy numbers;
  • Modification of entropy method using rough numbers;
  • Modification of entropy method using grey numbers;
  • Modification of entropy method using neutrosophic numbers;
  • Modification of entropy method using D-numbers;
  • Objective methods MCDM in different fields;
  • Comparisons of the entropy method with other MCDM methods;
  • Development of new methods MCDM;
  • MCDM in uncertain environments.

Dr. Darko Božanić
Guest Editor

Manuscript Submission Information

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Published Papers (6 papers)

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Research

21 pages, 4080 KiB  
Article
Extended Hellwig’s Method Utilizing Entropy-Based Weights and Mahalanobis Distance: Applications in Evaluating Sustainable Development in the Education Area
by Ewa Roszkowska, Marzena Filipowicz-Chomko, Anna Łyczkowska-Hanćkowiak and Elżbieta Majewska
Entropy 2024, 26(3), 197; https://doi.org/10.3390/e26030197 - 25 Feb 2024
Cited by 3 | Viewed by 1220
Abstract
One of the crucial steps in the multi-criteria decision analysis involves establishing the importance of criteria and determining the relationship between them. This paper proposes an extended Hellwig’s method (H_EM) that utilizes entropy-based weights and Mahalanobis distance to address this issue. By incorporating [...] Read more.
One of the crucial steps in the multi-criteria decision analysis involves establishing the importance of criteria and determining the relationship between them. This paper proposes an extended Hellwig’s method (H_EM) that utilizes entropy-based weights and Mahalanobis distance to address this issue. By incorporating the concept of entropy, weights are determined based on their information content represented by the matrix data. The Mahalanobis distance is employed to address interdependencies among criteria, contributing to the improved performance of the proposed framework. To illustrate the relevance and effectiveness of the extended H_EM method, this study utilizes it to assess the progress toward achieving Sustainable Development Goal 4 of the 2030 Agenda within the European Union countries for education in the year 2021. Performance comparison is conducted between results obtained by the extended Hellwig’s method and its other variants. The results reveal a significant impact on the ranking of the EU countries in the education area, depending on the choice of distance measure (Euclidean or Mahalanobis) and the system of weights (equal or entropy-based). Overall, this study highlights the potential of the proposed method in addressing complex decision-making scenarios with interdependent criteria. Full article
(This article belongs to the Special Issue Entropy Methods for Multicriteria Decision Making)
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13 pages, 1585 KiB  
Article
The Use of Information Entropy and Expert Opinion in Maximizing the Discriminating Power of Composite Indicators
by Matheus Pereira Libório, Roxani Karagiannis, Alexandre Magno Alvez Diniz, Petr Iakovlevitch Ekel, Douglas Alexandre Gomes Vieira and Laura Cozzi Ribeiro
Entropy 2024, 26(2), 143; https://doi.org/10.3390/e26020143 - 6 Feb 2024
Cited by 7 | Viewed by 1179
Abstract
This research offers a solution to a highly recognized and controversial problem within the composite indicator literature: sub-indicators weighting. The research proposes a novel hybrid weighting method that maximizes the discriminating power of the composite indicator with objectively defined weights. It considers the [...] Read more.
This research offers a solution to a highly recognized and controversial problem within the composite indicator literature: sub-indicators weighting. The research proposes a novel hybrid weighting method that maximizes the discriminating power of the composite indicator with objectively defined weights. It considers the experts’ uncertainty concerning the conceptual importance of sub-indicators in the multidimensional phenomenon, setting maximum and minimum weights (constraints) in the optimization function. The hybrid weighting scheme, known as the SAW-Max-Entropy method, avoids attributing weights that are incompatible with the multidimensional phenomenon’s theoretical framework. At the same time, it reduces the influence of assessment errors and judgment biases on composite indicator scores. The research results show that the SAW-Max-Entropy weighting scheme achieves greater discriminating power than weighting schemes based on the Entropy Index, Expert Opinion, and Equal Weights. The SAW-Max-Entropy method has high application potential due to the increasing use of composite indicators across diverse areas of knowledge. Additionally, the method represents a robust response to the challenge of constructing composite indicators with superior discriminating power. Full article
(This article belongs to the Special Issue Entropy Methods for Multicriteria Decision Making)
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19 pages, 849 KiB  
Article
Selection of an Insurance Company in Agriculture through Hybrid Multi-Criteria Decision-Making
by Adis Puška, Marija Lukić, Darko Božanić, Miroslav Nedeljković and Ibrahim M. Hezam
Entropy 2023, 25(6), 959; https://doi.org/10.3390/e25060959 - 20 Jun 2023
Cited by 2 | Viewed by 1439
Abstract
Crop insurance is used to reduce risk in agriculture. This research is focused on selecting an insurance company that provides the best policy conditions for crop insurance. A total of five insurance companies that provide crop insurance services in the Republic of Serbia [...] Read more.
Crop insurance is used to reduce risk in agriculture. This research is focused on selecting an insurance company that provides the best policy conditions for crop insurance. A total of five insurance companies that provide crop insurance services in the Republic of Serbia were selected. To choose the insurance company that provides the best policy conditions for farmers, expert opinions were solicited. In addition, fuzzy methods were used to assess the weights of the various criteria and to evaluate insurance companies. The weight of each criterion was determined using a combined approach based on fuzzy LMAW (the logarithm methodology of additive weights) and entropy methods. Fuzzy LMAW was used to determine the weights subjectively through expert ratings, while fuzzy entropy was used to determine the weights objectively. The results of these methods showed that the price criterion received the highest weight. The selection of the insurance company was made using the fuzzy CRADIS (compromise ranking of alternatives, from distance to ideal solution) method. The results of this method showed that the insurance company DDOR offers the best conditions for crop insurance for farmers. These results were confirmed by a validation of the results and sensitivity analysis. Based on all of this, it was shown that fuzzy methods can be used in the selection of insurance companies. Full article
(This article belongs to the Special Issue Entropy Methods for Multicriteria Decision Making)
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20 pages, 1282 KiB  
Article
The Role of Thermodynamic and Informational Entropy in Improving Real Estate Valuation Methods
by Ünsal Özdilek
Entropy 2023, 25(6), 907; https://doi.org/10.3390/e25060907 - 7 Jun 2023
Cited by 3 | Viewed by 1560
Abstract
Price, Cost and Income (PCI) are distinct economic indicators intrinsically linked to the values they denote. These observables take center stage in the multi-criteria decision-making process that enables economic agents to convey subjective utilities of market-exchanged commodities objectively. The valuation of these commodities [...] Read more.
Price, Cost and Income (PCI) are distinct economic indicators intrinsically linked to the values they denote. These observables take center stage in the multi-criteria decision-making process that enables economic agents to convey subjective utilities of market-exchanged commodities objectively. The valuation of these commodities heavily relies on PCI-based empirical observables and their supported methodologies. This valuation measure’s accuracy is critical, as it influences subsequent decisions within the market chain. However, measurement errors often arise due to inherent uncertainties in the value state, impacting economic agents’ wealth, particularly when trading significant commodities such as real estate properties. This paper addresses this issue by incorporating entropy measurements into real estate valuation. This mathematical technique adjusts and integrates triadic PCI estimates, improving the final stage of appraisal systems where definitive value decisions are crucial. Employing entropy within the appraisal system can also aid market agents in devising informed production/trading strategies for optimal returns. The results from our practical demonstration indicate promising implications. The entropy’s integration with PCI estimates significantly improved the value measurement’s precision and reduced economic decision-making errors. Full article
(This article belongs to the Special Issue Entropy Methods for Multicriteria Decision Making)
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26 pages, 1769 KiB  
Article
A Multicriteria-Based Comparison of Electric Vehicles Using q-Rung Orthopair Fuzzy Numbers
by Sanjib Biswas, Aparajita Sanyal, Darko Božanić, Samarjit Kar, Aleksandar Milić and Adis Puška
Entropy 2023, 25(6), 905; https://doi.org/10.3390/e25060905 - 6 Jun 2023
Cited by 6 | Viewed by 1187
Abstract
The subject of this research is the evaluation of electric cars and the choice of car that best meets the set research criteria. To this end, the criteria weights were determined using the entropy method with two-step normalization and a full consistency check. [...] Read more.
The subject of this research is the evaluation of electric cars and the choice of car that best meets the set research criteria. To this end, the criteria weights were determined using the entropy method with two-step normalization and a full consistency check. In addition, the entropy method was extended further with q-rung orthopair fuzzy (qROF) information and Einstein aggregation for carrying out decision making under uncertainty with imprecise information. Sustainable transportation was selected as the area of application. The current work compared a set of 20 leading EVs in India using the proposed decision-making model. The comparison was designed to cover two aspects: technical attributes and user opinions. For the ranking of the EVs, a recently developed multicriteria decision-making (MCDM) model, the alternative ranking order method with two-step normalization (AROMAN), was used. The present work is a novel hybridization of the entropy method, full consistency method (FUCOM), and AROMAN in an uncertain environment. The results show that the electricity consumption criterion (w = 0.0944) received the greatest weight, while the best ranked alternative was A7. The results also show robustness and stability, as revealed through a comparison with the other MCDM models and a sensitivity analysis. The present work is different from the past studies, as it provides a robust hybrid decision-making model that uses both objective and subjective information. Full article
(This article belongs to the Special Issue Entropy Methods for Multicriteria Decision Making)
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26 pages, 1191 KiB  
Article
Extended Multicriteria Group Decision Making with a Novel Aggregation Operator for Emergency Material Supplier Selection
by Ling Liu, Qiuyi Zhu, Dan Yang and Sen Liu
Entropy 2023, 25(4), 702; https://doi.org/10.3390/e25040702 - 21 Apr 2023
Cited by 2 | Viewed by 1558
Abstract
How to ensure the normal production of industries in an uncertain emergency environment has aroused a lot of concern in society. Selecting the best emergency material suppliers using the multicriteria group decision making (MCGDM) method will ensure the normal production of industries in [...] Read more.
How to ensure the normal production of industries in an uncertain emergency environment has aroused a lot of concern in society. Selecting the best emergency material suppliers using the multicriteria group decision making (MCGDM) method will ensure the normal production of industries in this environment. However, there are few studies in emergency environments that consider the impact of the decision order of decision makers (DMs) on the decision results. Therefore, in order to fill the research gap, we propose an extended MCGDM method, whose main steps include the following: Firstly, the DMs give their assessment of all alternatives. Secondly, we take the AHP method and entropy weight method to weight the criteria and the DMs. Thirdly, we take the intuitionistic fuzzy hybrid priority weight average (IFHPWA) operator we proposed to aggregate evaluation information and take the TOPSIS method to rank all the alternatives. Finally, the proposed method is applied in a case to prove its practicability and effectiveness. The proposed method considers the influence of the decision order of the DMs on the decision results, which improves the accuracy and efficiency of decision-making results. Full article
(This article belongs to the Special Issue Entropy Methods for Multicriteria Decision Making)
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