Information Measures And Ensemble Operators For Intuitionally Hesitant Fuzzy Sets And Their Applications

The theory of fuzzy set provides a broad development space for the application of multi-criteria decision making.As a new extension of fuzzy set,intuitionistic hesitant fuzzy set(IHFS)combines the advantages of intuitionistic fuzzy set and hesitant fuzzy set,and can deal with uncertain information more accurately and flexibly.How to fully mine the information of IHFS has become an important research direction.Based on this consideration,this paper studies the information measures and information integration operators on IHFS.The main work is as follows:1.This paper combines information content and information clarity differences based on aggregation function,and puts forward a construction method of distance measure and similarity measure for IHFS.This method can not only obtain some existing measures by selecting specific functions,but also construct new measures to obtain more objective results in pattern recognition.In addition,the axiomatic definition of intuitionistic hesitant fuzzy entropy measure is given,and the transformation relations among distance measure,similarity measure and entropy measure are studied accordingly.Finally,according to the new distance measure and entropy measure,an extended technique for order preference by similarity to ideal solution(TOPSIS)method is designed to solve the multi-criteria decision making problem,and the effectiveness of the proposed method is demonstrated.2.In this paper,the generalized Maclaurin symmetric mean(GMSM)operator is introduced into the intuitionistic hesitant fuzzy environment by combining the idea of Archimedes norm,and the intuitionistic hesitant generalized Maclaurin symmetric mean operator and the weighted operator are proposed.Moreover,the idempotency,monotony and degenerate properties of the operator are studied,and some special expressions of the operator arc obtained by selecting different parameters or operating rules.Finally,a multi-criteria group decision making model is constructed based on the proposed operator,and its practicability and flexibility are illustrated by a concrete example.