Entropy Of Dual Hesitation Fuzzy Sets And Its Application In Multi - Attribute Decision Making

In fuzzy set theory, entropy is an very important notion for measuring uncertain information. Hesitant fuzzy set and dual hesitant fuzzy set are new general forms of fuzzy set. This paper deals with axiomatic definition of entropy, entropy measures for hesitant fuzzy set and dual hesitant fuzzy set, and their application in multiple attribute decision-making. It consists of three chapters.In chapter 1, we introduce the research background and development status of hesitant fuzzy sets and dual hesitant fuzzy sets, and the main result of this thesis.In chapter 2, we study the entropy theory of hesitant fuzzy sets and their application in group decision-making. Firstly, we propose the axiomatic definition of entropy and entropy measures for hesitant fuzzy elements and hesitant fuzzy sets, respectively, based on their own fuzziness and hesitation. Then, we give the comparison between the proposed theory and relevant definitions in the existing literatures. The result shows that the proposed entropy axiomatic definition can not only consider the fuzziness of hesitant fuzzy elements but also the hesitation of them; and the proposed entropy measure can distinguish the degree of uncertainty for hesitant fuzzy elements more effectively. We also propose a general form of entropy measures for hesitant fuzzy sets. At last, we present a hesitant fuzzy group decision-making method.In chapter 3, we study the entropy theory of dual hesitant fuzzy sets and its application in multi-attribute decision-making. We firstly propose the axiomatic definition of entropy and entropy measures for dual hesitant fuzzy elements. Based on these, we present the axiomatic definition of entropy and entropy measures for dual hesitant fuzzy sets in order to perfect the entropy theory of dual hesitant fuzzy sets. Finally, a practical example of dual hesitant fuzzy multiple attribute decision-making problem is given to demonstrate the practicality and effectiveness of the developed entropy measures.