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Entropy
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Entropy in the Decision-Making Problems under Uncertain Environments
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Entropy in the Decision-Making Problems under Uncertain Environments

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

Deadline for manuscript submissions: closed (20 May 2022) | Viewed by 8891

Special Issue Editor

Dr. Wojciech Sałabun

E-Mail Website
Guest Editor
Department of Artificial Intelligence method and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, ul. Żołnierska 49, 71-210 Szczecin, Poland
Interests: decision support system; decision making; MCDA; fuzzy logic; artificial intelligence
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The uncertainty of decision-making attributes and criterion weights are significant challenges in current research trends. Researchers using various generalizations of soft computing and entropy are getting increasingly effective approaches to solving complex decision-making problems. Modern decision-making methods are particularly welcome, which is understood as the collection of single or multicriteria techniques aiming at selecting the best alternative in case of imprecise, incomplete, and vague data. Any type of research related to the effectiveness of entropy in decision-making is also welcome. Uncertainty and its role in decision-making is an important phenomenon that has received considerable research attention in many branches of science. Therefore, in this Special Issue, we shall encourage the submission of papers devoted to the adaptation of entropy to the solution of decision-making problems in the presence of modern types of uncertainty. However, we will also consider interesting and valuable papers where the problem of uncertainty is solved by using a soft computing or generalization of fuzzy sets theory with the implicit use of entropy techniques.

Dr. Wojciech Sałabun
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. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

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Published Papers (3 papers)

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Research

32 pages, 781 KiB  
Article
Fermatean Fuzzy Schweizer–Sklar Operators and BWM-Entropy-Based Combined Compromise Solution Approach: An Application to Green Supplier Selection
by Dongmei Wei, Dan Meng, Yuan Rong, Yi Liu, Harish Garg and Dragan Pamucar
Entropy 2022, 24(6), 776; https://doi.org/10.3390/e24060776 - 31 May 2022
Cited by 34 | Viewed by 3040
Abstract
The Fermatean fuzzy set (FFS) is a momentous generalization of a intuitionistic fuzzy set and a Pythagorean fuzzy set that can more accurately portray the complex vague information of elements and has stronger expert flexibility during decision analysis. The Combined Compromise Solution (CoCoSo) [...] Read more.
The Fermatean fuzzy set (FFS) is a momentous generalization of a intuitionistic fuzzy set and a Pythagorean fuzzy set that can more accurately portray the complex vague information of elements and has stronger expert flexibility during decision analysis. The Combined Compromise Solution (CoCoSo) approach is a powerful decision-making technique to choose the ideal objective by fusing three aggregation strategies. In this paper, an integrated, multi-criteria group-decision-making (MCGDM) approach based on CoCoSo and FFS is used to assess green suppliers. To begin, several innovative operations of Fermatean fuzzy numbers based on Schweizer–Sklar norms are presented, and four aggregation operators utilizing the proposed operations are also developed. Several worthwhile properties of the advanced operations and operators are explored in detail. Next, a new Fermatean fuzzy entropy measure is propounded to determine the combined weight of criteria, in which the subjective and objective weights are computed by an improved best-and-worst method (BWM) and entropy weight approach, respectively. Furthermore, MCGDM based on CoCoSo and BWM-Entropy is brought forward and employed to sort diverse green suppliers. Lastly, the usefulness and effectiveness of the presented methodology is validated by comparison, and the stability of the developed MCGDM approach is shown by sensitivity analysis. The results shows that the introduced method is more stable during ranking of green suppliers, and the comparative results expound that the proposed method has higher universality and credibility than prior Fermatean fuzzy approaches. Full article
(This article belongs to the Special Issue Entropy in the Decision-Making Problems under Uncertain Environments)
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16 pages, 427 KiB  
Article
New Pythagorean Entropy Measure with Application in Multi-Criteria Decision Analysis
by Neeraj Gandotra, Bartłomiej Kizielewicz, Abhimanyu Anand, Aleksandra Bączkiewicz, Andrii Shekhovtsov, Jarosław Wątróbski, Akbar Rezaei and Wojciech Sałabun
Entropy 2021, 23(12), 1600; https://doi.org/10.3390/e23121600 - 29 Nov 2021
Cited by 22 | Viewed by 3031
Abstract
The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that [...] Read more.
The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The performance of the introduced method is illustrated in a real-life case study, including a multi-criteria company selection problem. In this example, we provide a numerical illustration to distinguish the entropy measure proposed from some existing entropies used for Pythagorean fuzzy sets and intuitionistic fuzzy sets. Statistical illustrations show that the proposed entropy measures are reliable for demonstrating the degree of fuzziness of both Pythagorean fuzzy set (PFS) and intuitionistic fuzzy sets (IFS). In addition, a multi-criteria decision-making method complex proportional assessment (COPRAS) was also proposed with weights calculated based on the proposed new entropy measure. Finally, to validate the reliability of the results obtained using the proposed entropy, a comparative analysis was performed with a set of carefully selected reference methods containing other generally used entropy measurement methods. The illustrated numerical example proves that the calculation results of the proposed new method are similar to those of several other up-to-date methods. Full article
(This article belongs to the Special Issue Entropy in the Decision-Making Problems under Uncertain Environments)
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23 pages, 360 KiB  
Article
A Novel q-Rung Dual Hesitant Fuzzy Multi-Attribute Decision-Making Method Based on Entropy Weights
by Yaqing Kou, Xue Feng and Jun Wang
Entropy 2021, 23(10), 1322; https://doi.org/10.3390/e23101322 - 11 Oct 2021
Cited by 8 | Viewed by 1888
Abstract
In this paper, a new multiple attribute decision-making (MADM) method under q-rung dual hesitant fuzzy environment from the perspective of aggregation operators is proposed. First, some aggregation operators are proposed for fusing q-rung dual hesitant fuzzy sets (q-RDHFSs). Afterwards, we present properties and [...] Read more.
In this paper, a new multiple attribute decision-making (MADM) method under q-rung dual hesitant fuzzy environment from the perspective of aggregation operators is proposed. First, some aggregation operators are proposed for fusing q-rung dual hesitant fuzzy sets (q-RDHFSs). Afterwards, we present properties and some desirable special cases of the new operators. Second, a new entropy measure for q-RDHFSs is developed, which defines a method to calculate the weight information of aggregated q-rung dual hesitant fuzzy elements. Third, a novel MADM method is introduced to deal with decision-making problems under q-RDHFSs environment, wherein weight information is completely unknown. Finally, we present numerical example to show the effectiveness and performance of the new method. Additionally, comparative analysis is conducted to prove the superiorities of our new MADM method. This study mainly contributes to a novel method, which can help decision makes select optimal alternatives when dealing with practical MADM problems. Full article
(This article belongs to the Special Issue Entropy in the Decision-Making Problems under Uncertain Environments)
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