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Knowledge measure of hesitant fuzzy set and its application in multi-attribute decision-making

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Abstract

The fuzzy knowledge measure is considered as a dual measure of fuzzy entropy. In this work, we introduce an axiomatic framework to define a hesitant fuzzy knowledge measure (HF-knowledge measure) and investigate hesitant fuzzy entropy (HF-entropy) and HF-knowledge measure from the viewpoint of duality. We provide a characterization result to obtain a class of the HF-knowledge measure. We also obtain an HF-knowledge measure from similarity and dissimilarity measures of hesitant fuzzy sets. Here, we introduce an HF-knowledge measure and show its effectiveness with the help of an illustrative example from the viewpoint of linguistic hedges. We apply the proposed HF-knowledge measure to multiple-attribute decision-making (MADM) problem by utilizing the TOPSIS method and justify its advantage over existing HF-entropies.

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Acknowledgements

The authors would like to thank the editor and anonymous referees for their helpful and constructive suggestions.

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Authors and Affiliations

  1. School of Mathematics, Shri Mata Vaishno Devi University, Katra, Jammu and Kashmir, 182320, India

    Sumita Lalotra & Surender Singh

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  1. Sumita Lalotra
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  2. Surender Singh
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Correspondence to Surender Singh.

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Communicated by Anibal Tavares de Azevedo.

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Lalotra, S., Singh, S. Knowledge measure of hesitant fuzzy set and its application in multi-attribute decision-making. Comp. Appl. Math. 39, 86 (2020). https://doi.org/10.1007/s40314-020-1095-y

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