Intuitionistic Fuzzy Divergence Measure Based On Several Kinds Of Chi-square Distribution And Its Application

The intuitionist,ic fuzzy sets,as a generalization of fuzzy sets,could provide the information on the membership degree,the non-membership degree and the h-esitancy degree,it should have better flexibility and practicability than traditional fuzzy sets in processing uncertain and imprecise problems.On the other hand,the divergence measure,as a useful tool to measure the differences between informa-tion,is widely used in classification problems.Many scholars have done a lot of work around its axiomatic definition and divergence formula,and it has been widely used in many fields such as multi-attribute decision-making and pattern recogni-tion.In this paper,on the basis of axiomatic definition of divergence measure for intuitionistic fuzzy set,several intuitionistic fuzzy divergence measures and an en-tropy measure based on Chi-square distribution are presented and the relationship between divergence measure and entropy measure are discussed,additionally,some properties of the proposed divergence are given and the conclusion can be directly applied to recommendation system and pattern recognitionFirst of all,according to the structure characteristic of intuitionistic fuzzy sets,the divergence of Dragomir's random distribution is transformed into the divergence between intuitionistic fuzzy sets and the properties of the proposed divergence is s-tudied.Numerical example are given to illustrate the application of the proposed divergence in recommendation systemSecondly,corresponding to the methods of Vlachos and Sergiadis,an entropy measure of intuitionistic fuzzy set is given and a weighted intuitionistic fuzzy di-vergence measure based on Chi-square distribution is proposed by combining with Shapley functionFinally,the proposed intuitionistic fuzzy divergence measure is extended to an interval valued intuitionistic fuzzy divergence measure based on Chi-square distribu-tion,two numerical examples are given to illustrate the application of the proposed divergence measure of interval valued intuitionistic fuzzy sets to pattern recognition and multi-attribute decision-making.