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Relative-distance-based approaches for ranking intuitionistic fuzzy values

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Abstract

During the uncertain information processing on Atanassov’s intuitionistic fuzzy sets, the ranking for intuitionistic fuzzy values (IFVs) is an important and omnipresent issue. Even though many orders used to compare any two IFVs have been proposed, some shortcomings, such as inadmissibility, nonrobustness, and nondeterminacy, may exist when these orders are utilized. Inspired by the Euclidean approach for ranking IFVs, we present a novel order that can overcome the aforementioned shortcomings using the notion of relative geometric distance. With the help of graphic representation of an IFV, we analyze the existing popular approaches for ranking IFVs and point out their drawbacks. Taking into account these three distances between an IFV and the ideal negative point, ideal positive point and most uncertain point, respectively, we present a relative-distance-based mensuration for describing the favorable degree of the IFV. Accordingly, the boundaries used in the existing ranking approaches for IFVs are replaced by a novel curve. We prove that the proposed method satisfies the admissibility, robustness, and determinacy requirements. Finally, we extend the presented ranking method for IFVs by introducing human attitudes and compare the proposed approach with the existing ones, which indicates its availability and rationality. We then can obtain the conclusion that the relative distance is an effective and reasonable approach for ranking IFVs.

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Acknowledgements

This work was supported by the Natural Science Foundation of China (Grant Nos. 71671086 and 71201076), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (no. 20KJA520006), the Foundation for Young Talents in Higher Education of Guangdong Province (No. 2019WQNCX027) and the Start-up Research Science Fund of Shantou University (No. STF19025)

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Authors and Affiliations

  1. School of Information Engineering, Nanjing Audit University, Nanjing, 211815, People’s Republic of China

    Bing Huang & Guofu Feng

  2. Business School, Shantou University, Shantou, 515063, People’s Republic of China

    Jiubing Liu

  3. Business School, Sichuan University, Chengdu, 610064, People’s Republic of China

    Chunxiang Guo

  4. School of Management and Engineering, Nanjing University, Nanjing, 210093, People’s Republic of China

    Huaxiong Li

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  1. Bing Huang
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  2. Jiubing Liu
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  3. Chunxiang Guo
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  4. Huaxiong Li
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  5. Guofu Feng
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Correspondence to Bing Huang or Chunxiang Guo.

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Huang, B., Liu, J., Guo, C. et al. Relative-distance-based approaches for ranking intuitionistic fuzzy values. Artif Intell Rev 54, 3089–3114 (2021). https://doi.org/10.1007/s10462-020-09921-7

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