The general formula of entropy and similarity measures for hesitant fuzzy linguistic term sets

Abstract

In order to quantitatively characterize the uncertainty of hesitant fuzzy linguistic information, the entropy and similarity measures of hesitant fuzzy linguistic term sets are studied. First, the axiomatic definitions of entropy and similarity measures of hesitant fuzzy linguistic term sets are given, and general formulas of entropy and similarity measures for hesitant fuzzy linguistic term sets are proposed. Moreover, the algorithms for generating entropy and similarity of hesitant fuzzy linguistic term set are given. Then the relationship between entropy and similarity of hesitant fuzzy linguistic term set is studied, and the general formula of entropy based on similarity is proposed. These lay the theoretical foundation for flexible selection of entropy and similarity in multi-attribute decision making.