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

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.