Intuitionistic Fuzzy Entropy, Interval-valued Intuitionistic Fuzzy Entropy And Its Application

This thesis investigates the intuitionistic fuzzy entropy, interval-valued intu-itionistic fuzzy entropy and its application. It consists of four chapters.In the first chapter, we mainly introduce the origin and current research situations of intuitionsitic fuzzy entropy and interval-valued intuitionsitic fuzzy entropy. Then we list the main achievement of this paper.In chapter 2, we investigate the problem of intuitionistic fuzzy entropy. We give an intuitionistic fuzzy entropy formula based on trigonometric function. Then, two ntuitionistic fuzzy entropy formula which proposed by Ye are discussed and proved that they are equivalence. We compare the formula we proposed with other intuitionistic fuzzy entropy formula, and numerical examples were given to show that the proposed measures are reasonable and effective.In chapter 3, we introduce an interval-valued intuitionistic fuzzy entropy formula based on the entropy measure for IFSs which proposed in the second chapter. We prove that the proposed interval-valued intuitionistic fuzzy entropy formula satisfy the axiomatic definitions of interval-valued intuitionistic fuzzy entropy. We also compare the proposed formula with two interval-valued intu-itionistic fuzzy entropy fomula based on trigonometric function which are given by Ye.In the last chapter, we discuss the interval-valued intuitionistic fuzzy entropy formula based on Hamming distance. We fist improve the Hamming distance formula for two interval-valued intuitionistic fuzzy sets. Then, we give an interval- valued intuitionistic fuzzy entropy formula based on Hamming distance. Afterthat we propose an effective method to deal with interval-valued intuitionisticfuzzy set multiple attribute decision making problem with unknown weights.