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Construction methods for entropy measures of circular intuitionistic fuzzy sets and their application.

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Title: Construction methods for entropy measures of circular intuitionistic fuzzy sets and their application.
Authors: Khan, Muhammad Jabir1 (AUTHOR) jabirkhan.uos@gmail.com, Jiang, Shu1 (AUTHOR) jshmjs45@gmail.com, Ding, Weiping1,2 (AUTHOR) dwp9988@163.com, Akram, Muhammad3 (AUTHOR) m.akram@pucit.edu.pk
Source: Engineering Applications of Artificial Intelligence. Nov2025:Part A, Vol. 160, pN.PAG-N.PAG. 1p.
Subjects: TOPSIS method, Aggregation operators, Multiple criteria decision making, Fuzzy sets, Triangular norms, Information measurement
Abstract: The circular intuitionistic fuzzy set (C-IFS) is a recent extension of the intuitionistic fuzzy set, whose elements are represented as circles instead of specific orthopairs. Entropy measures provide us with a quantitative measure of uncertainty. This research addresses the gap in entropy measures for C-IFSs by introducing innovative construction methods. It establishes robust theoretical frameworks for entropy measures, leveraging established mathematical concepts including t-norms, t-conorms, automorphisms, and aggregation operators. It provides several proven mathematical results and expressions for entropy measures. Moreover, it is worth mentioning that entropy measures can be generated not only using t-norms and t-conorms alone but also when coupled with automorphisms and aggregation operators. Additionally, the argument formulation of t-norms and t-conorms plays a significant role in entropy measure generation, and these formulations are not unique, thereby paving the way for future research avenues. In addition to these contributions, a novel transformation method from entropy to a similarity measure is proposed. This transformation method fully incorporates all aspects of C-IFSs. Lastly, the technique for order preference by similarity to ideal solution (TOPSIS) is extended for C-IFSs to deal with multi-criteria decision-making problems and overcome its previous extensions' limitations. This method consists of a novel criteria weight generation method that is entropy-based and the modified relative closeness index, adding further depth to the approach. Various numerical examples are given to elaborate on our results. • Developed construction methods for entropy measures of circular intuitionistic fuzzy set. • Uses t-norm, t-conorm, automorphism, and aggregation operator for entropy developments. • Proposed a transformation technique to derive similarity measures from entropy measures. • Extended the TOPSIS method to address decision-making problems. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:The circular intuitionistic fuzzy set (C-IFS) is a recent extension of the intuitionistic fuzzy set, whose elements are represented as circles instead of specific orthopairs. Entropy measures provide us with a quantitative measure of uncertainty. This research addresses the gap in entropy measures for C-IFSs by introducing innovative construction methods. It establishes robust theoretical frameworks for entropy measures, leveraging established mathematical concepts including t-norms, t-conorms, automorphisms, and aggregation operators. It provides several proven mathematical results and expressions for entropy measures. Moreover, it is worth mentioning that entropy measures can be generated not only using t-norms and t-conorms alone but also when coupled with automorphisms and aggregation operators. Additionally, the argument formulation of t-norms and t-conorms plays a significant role in entropy measure generation, and these formulations are not unique, thereby paving the way for future research avenues. In addition to these contributions, a novel transformation method from entropy to a similarity measure is proposed. This transformation method fully incorporates all aspects of C-IFSs. Lastly, the technique for order preference by similarity to ideal solution (TOPSIS) is extended for C-IFSs to deal with multi-criteria decision-making problems and overcome its previous extensions' limitations. This method consists of a novel criteria weight generation method that is entropy-based and the modified relative closeness index, adding further depth to the approach. Various numerical examples are given to elaborate on our results. • Developed construction methods for entropy measures of circular intuitionistic fuzzy set. • Uses t-norm, t-conorm, automorphism, and aggregation operator for entropy developments. • Proposed a transformation technique to derive similarity measures from entropy measures. • Extended the TOPSIS method to address decision-making problems. [ABSTRACT FROM AUTHOR]
ISSN:09521976
DOI:10.1016/j.engappai.2025.111809