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Centroid Transformations of Intuitionistic Fuzzy Values Based on Aggregation Operators

Author

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  • Xiaoyan Liu

    (Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China)

  • Hee Sik Kim

    (Department of Mathematics, Research Institute of Natural Sciences, Hanyang University, Seoul 04763, Korea)

  • Feng Feng

    (Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
    Shaanxi Key Laboratory of Network Data Analysis and Intelligent Processing, Xi’an University of Posts and Telecommunications, Xi’an 710121, China)

  • José Carlos R. Alcantud

    (BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, E37007 Salamanca, Spain)

Abstract

Atanassov’s intuitionistic fuzzy sets extend the notion of fuzzy sets. In addition to Zadeh’s membership function, a non-membership function is also considered. Intuitionistic fuzzy values play a crucial role in both theoretical and practical progress of intuitionistic fuzzy sets. This study introduces and explores various types of centroid transformations of intuitionistic fuzzy values. First, we present some new concepts for intuitionistic fuzzy values, including upper determinations, lower determinations, spectrum triangles, simple intuitionistic fuzzy averaging operators and simply weighted intuitionistic fuzzy averaging operators. With the aid of these notions, we construct centroid transformations, weighted centroid transformations, simple centroid transformations and simply weighted centroid transformations. We provide some basic characterizations regarding various types of centroid transformations, and show their difference using an illustrating example. Finally, we focus on simple centroid transformations and investigate the limit properties of simple centroid transformation sequences. Among other facts, we show that a simple centroid transformation sequence converges to the simple intuitionistic fuzzy average of the lower and upper determinations of the first intuitionistic fuzzy value in the sequence.

Suggested Citation

  • Xiaoyan Liu & Hee Sik Kim & Feng Feng & José Carlos R. Alcantud, 2018. "Centroid Transformations of Intuitionistic Fuzzy Values Based on Aggregation Operators," Mathematics, MDPI, vol. 6(11), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:11:p:215-:d:177913
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    References listed on IDEAS

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    1. José Alcantud & Annick Laruelle, 2014. "Dis&approval voting: a characterization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 1-10, June.
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    Cited by:

    1. Anam Luqman & Muhammad Akram & Ahmad N. Al-Kenani, 2019. "q -Rung Orthopair Fuzzy Hypergraphs with Applications," Mathematics, MDPI, vol. 7(3), pages 1-22, March.
    2. Feng Feng & Yujuan Zheng & José Carlos R. Alcantud & Qian Wang, 2020. "Minkowski Weighted Score Functions of Intuitionistic Fuzzy Values," Mathematics, MDPI, vol. 8(7), pages 1-30, July.
    3. Mohammed Alqahtani & M. Kaviyarasu & Anas Al-Masarwah & M. Rajeshwari, 2024. "Application of Complex Neutrosophic Graphs in Hospital Infrastructure Design," Mathematics, MDPI, vol. 12(5), pages 1-23, February.
    4. Gulfam Shahzadi & Muhammad Akram & Ahmad N. Al-Kenani, 2020. "Decision-Making Approach under Pythagorean Fuzzy Yager Weighted Operators," Mathematics, MDPI, vol. 8(1), pages 1-20, January.

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