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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]
Copyright of Engineering Applications of Artificial Intelligence is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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  Data: Construction methods for entropy measures of circular intuitionistic fuzzy sets and their application.
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  Data: <searchLink fieldCode="AR" term="%22Khan%2C+Muhammad+Jabir%22">Khan, Muhammad Jabir</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jabirkhan.uos@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Jiang%2C+Shu%22">Jiang, Shu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jshmjs45@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Ding%2C+Weiping%22">Ding, Weiping</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> dwp9988@163.com</i><br /><searchLink fieldCode="AR" term="%22Akram%2C+Muhammad%22">Akram, Muhammad</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> m.akram@pucit.edu.pk</i>
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  Data: <searchLink fieldCode="JN" term="%22Engineering+Applications+of+Artificial+Intelligence%22">Engineering Applications of Artificial Intelligence</searchLink>. Nov2025:Part A, Vol. 160, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22TOPSIS+method%22">TOPSIS method</searchLink><br /><searchLink fieldCode="DE" term="%22Aggregation+operators%22">Aggregation operators</searchLink><br /><searchLink fieldCode="DE" term="%22Multiple+criteria+decision+making%22">Multiple criteria decision making</searchLink><br /><searchLink fieldCode="DE" term="%22Fuzzy+sets%22">Fuzzy sets</searchLink><br /><searchLink fieldCode="DE" term="%22Triangular+norms%22">Triangular norms</searchLink><br /><searchLink fieldCode="DE" term="%22Information+measurement%22">Information measurement</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Engineering Applications of Artificial Intelligence is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.engappai.2025.111809
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      – Code: eng
        Text: English
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      – SubjectFull: Aggregation operators
        Type: general
      – SubjectFull: Multiple criteria decision making
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      – SubjectFull: Fuzzy sets
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      – SubjectFull: Triangular norms
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      – SubjectFull: Information measurement
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      – TitleFull: Construction methods for entropy measures of circular intuitionistic fuzzy sets and their application.
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            NameFull: Khan, Muhammad Jabir
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            NameFull: Jiang, Shu
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            NameFull: Ding, Weiping
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              Text: Nov2025:Part A
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              Value: 160
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