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An approach to construct entropies on interval-valued intuitionistic fuzzy sets by their distance functions

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Abstract

The main contribution of this paper is to give a new axiomatic definition of entropy measure and provide a constructing approach in the context of interval-valued intuitionistic fuzzy set (IVIFS). We give a new idea to define entropy on IVIFS: From the graphical representation, we consider the difference between a given IVIFS and its corresponding two interval fuzzy sets (IVFSs) by introducing a distance function that meets some specific conditions. The relationship between the distance function and the distance measure has also been illustrated. Based on distance functions, we give an approach to construct entropy measures on IVIFS. Then, a plenty of new entropies on IVIFS are introduced. Furthermore, we use a comparative example to show the proposed measures outperform the existing measures and utilize a demonstrative example to explain the application of the entropy measure in the multi-criteria decision making (MCDM), which verify the feasibility of our entropy construction method.

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Acknowledgements

The authors would like to thank the anonymous referees for helping them refine the ideas presented in this paper and improve the clarity of the presentation. This paper was supported by National Science Foundation of China (Grant Nos.: 11671244, 12071271) and the Higher School Doctoral Subject Foundation of Ministry of Education of China (Grant No.: 20130202110001).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, Shaanxi, People’s Republic of China

    Renqing Che, Chunfeng Suo & Yongming Li

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  1. Renqing Che
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  2. Chunfeng Suo
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  3. Yongming Li
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Contributions

RC and CS contributed to study conception and design. RC and YL contributed to analysis and interpretation of data. RC and CS contributed to programming. RC, CS and YL contributed to drafting of manuscript. RC, CS and YL contributed to critical revision.

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Correspondence to Yongming Li.

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Che, R., Suo, C. & Li, Y. An approach to construct entropies on interval-valued intuitionistic fuzzy sets by their distance functions. Soft Comput 25, 6879–6889 (2021). https://doi.org/10.1007/s00500-021-05713-5

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