A Study On The Measurement Of Hesitant Intuition Fuzzy Information And Its Application In Multi-attribute Decision-making

The hesitant intuitionistic fuzzy set integrates the advantages of the intuitionistic fuzzy set and the hesitant fuzzy set,and can deal with the problems with inconsistent preferences of decision makers in decision making process effectively.Considering that people have different psychological preferences,the supporting degree of evaluation values is also different.Therefore,the probability hesitant intuitionistic fuzzy set is introduced,which is more suitable for the decision making environment of real world when describing uncertain information.The knowledge measure was proposed by Szmidt as duality of entropy measure in 2012.And it is more intuitive and flexible when measuring and describing hesitant intuitionistic fuzzy information.This paper mainly studies the knowledge measure of the hesitant intuitionistic fuzzy set and probability hesitant intuitionistic fuzzy set and their applications in multi-attribute decision making theory.The main research works are as follows:1.Based on the information content and information clarity of the hesitant intuitionistic fuzzy set,a class of knowledge measure models with attitude coefficient is developed.Furthermore,it is verified that the knowledge measure is proportional to the change of the parameter and can avoid the influence of people’s psychological preferences in decision making process.2.The axiomatic definition of the knowledge measure of the probabilistic hesitant intuitionistic fuzzy set is proposed.A class of knowledge measure models is constructed based on the distance measure,and three special kinds of the knowledge measure are obtained by taking specific real functions for this model so that the nature of these knowledge measures is studied in detail.3.The application of knowledge measures of the hesitant intuitionistic fuzzyset and the probabilistic hesitant intuitionistic fuzzy set to multi-attribute decision making has been given,and the effectiveness and rationality of the proposed knowledge measures are demonstrated with specific examples.Furthermore,through comparative analysis,it is obtained that the multi-attribute decision making method based on the probabilistic hesitant intuitionistic fuzzy set is more practical and has a wider application prospect.