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New hesitation-based distance and similarity measures on intuitionistic fuzzy sets and their applications

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  • Yun Kang
  • Shunxiang Wu
  • Da Cao
  • Wei Weng

Abstract

In this paper, we present new definitions on distance and similarity measures between intuitionistic fuzzy sets (IFSs) by combining with hesitation degree. First, we discuss the limitations in traditional distance and similarity measures, which are caused by the neglect of hesitation degree's influence. Even though a vector-valued similarity measure was proposed, which has two components indicating similarity and hesitation aspects, it still cannot perform well in practical applications because hesitation works only when the values of similarity measures are equal. In order to overcome the limitations, we propose new definitions on hesitation, distance and similarity measures, and research some theorems which satisfy the requirements of the proposed definitions. Meanwhile, we investigate the relationships among hesitation, distance, similarity and entropy of IFSs to verify the consistency of our work and previous research. Finally, we analyse and discuss the advantages and disadvantages of the proposed similarity measure in detail, and then we apply the proposed measures (dH and SH) to deal with pattern recognition problems, and demonstrate that they outperform state-of-the-art distance and similarity measures.

Suggested Citation

  • Yun Kang & Shunxiang Wu & Da Cao & Wei Weng, 2018. "New hesitation-based distance and similarity measures on intuitionistic fuzzy sets and their applications," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(4), pages 783-799, March.
    • Handle: RePEc:taf:tsysxx:v:49:y:2018:i:4:p:783-799
    DOI: 10.1080/00207721.2018.1424965
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    Cited by:

    1. Yanran Hong & Dongsheng Xu & Kaili Xiang & Han Qiao & Xiangxiang Cui & Huaxiang Xian, 2019. "Multi-Attribute Decision-Making Based on Preference Perspective with Interval Neutrosophic Sets in Venture Capital," Mathematics, MDPI, vol. 7(3), pages 1-13, March.

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