Methods Of Interval-valued Intuitionistic Fuzzy Information Measure

This thesis deals with the methods of interval-valued intuitionistic fuzzy information measure. It consists of four chapters.In the first chapter, we mainly introduce the origin and current research situations of interval-valued intuitionsitic fuzzy information measure. Then we list the main achievement of this paper.In chapter 2, we investigate the problem of interval-valued intuitionistic fuzzy entropy. We point out that three formulas of intuitionistic fuzzy entropy are equivalent. By extending the formula of intuitionistic fuzzy entropy to interval-valued intuitionistic fuzzy sets, the formula of interval-valued intuitionistic fuzzy entropy is introduced, and it satisfies four axiomatic requirements of interval-valued intuitionistic fuzzy entropy.In chapter 3, we introduce interval-valued intuitionistic fuzzy cross-entropy and its applications to multi-criteria fuzzy decision making. Firstly, we generalize the intuitionistic fuzzy cross-entropy defined by Vlochos and Sergiadis [Intuition-istic fuzzy information-Applications to pattern recognition, Pattern Recognition Letters,2007,28:197-206] to interval-valued intuitionistic fuzzy sets and define interval-valued intuitionistic fuzzy cross-entropy. Based on the concept of this cross-entropy, we give a formula of interval-valued intuitionistic fuzzy entropy. Finally, we propose a new handling method to multi-criteria fuzzy decision mak-ing by using interval-valued intuitionistic fuzzy cross-entropy and adopt several illustrative examples to demonstrate the practicability and effectuality of the proposed approach.In the last chapter, we discuss the relationship between similarity measure and entropy of interval-valued intuitionistic fuzzy sets in detail, and prove some theorems that similarity measure and entropy of interval-valued intuitionsitic fuzzy sets can be transformed by each other based on their axiomatic definitions. By using their relationship, we investigate a certain similarity measure formula of intuitionistic fuzzy sets. Several illustrative examples are given to demonstrate the practicality and effectiveness of the proposed formula. As applications, we use the similarity measure to solve some problems on multicriteria fuzzy decision making.