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Distance-Based Knowledge Measure and Entropy for Interval-Valued Intuitionistic Fuzzy Sets

Author

Listed:
  • Chunfeng Suo

    (School of Mathematics and Statistics, Beihua University, Jilin 132000, China)

  • Xuanchen Li

    (School of Mathematics and Statistics, Beihua University, Jilin 132000, China)

  • Yongming Li

    (School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China)

Abstract

The knowledge measure or uncertainty measure for constructing interval-valued intuitionistic fuzzy sets has attracted much attention. However, many uncertainty measures are measured by the entropy of interval-valued intuitionistic fuzzy sets, which cannot adequately reflect the knowledge of interval-valued intuitionistic fuzzy sets. In this paper, we not only extend the axiomatic definition of the knowledge measure of the interval-valued intuitionistic fuzzy set to a more general level but also establish a new knowledge measure function complying with the distance function combined with the technique for order preference by similarity to ideal solution (TOPSIS). Further, we investigate the properties of the proposed knowledge measure based on mathematical analysis and numerical examples. In addition, we create the entropy function by calculating the distance from the interval-valued fuzzy set to the most fuzzy point and prove that it satisfies the axiomatic definition. Finally, the proposed entropy is applied to the multi-attribute group decision-making problem with interval-valued intuitionistic fuzzy information. Experimental results demonstrate the effectiveness and practicability of the proposed entropy measure.

Suggested Citation

  • Chunfeng Suo & Xuanchen Li & Yongming Li, 2023. "Distance-Based Knowledge Measure and Entropy for Interval-Valued Intuitionistic Fuzzy Sets," Mathematics, MDPI, vol. 11(16), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3468-:d:1214774
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    References listed on IDEAS

    as
    1. Xiaohong Chen & Li Yang & Pei Wang & Wei Yue, 2013. "A Fuzzy Multicriteria Group Decision-Making Method with New Entropy of Interval-Valued Intuitionistic Fuzzy Sets," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, May.
    2. Yingjun Zhang & Peihua Li & Yizhi Wang & Peijun Ma & Xiaohong Su, 2013. "Multiattribute Decision Making Based on Entropy under Interval-Valued Intuitionistic Fuzzy Environment," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-8, September.
    3. Cuiping Wei & Yuzhong Zhang, 2015. "Entropy Measures for Interval-Valued Intuitionistic Fuzzy Sets and Their Application in Group Decision-Making," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-13, January.
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