Research On Ranking Method And Entropy Measure Of Interval-valued Intuitionistic Fuzzy Sets

Compared to fuzzy sets,intuitionistic fuzzy sets and interval numbers,interval-valued intuitionistic fuzzy sets has more flexibility and practicality in dealing with fuzzy or uncertain information.It has been widely used in practical issues such as decision analysis,pattern recognition,and supplier selection.In this paper,focus of research on multi-attribute group decision making problems based on interval-valued intuitionistic fuzzy sets--the ranking method and entropy measure of interval-valued intuitionistic fuzzy sets are studied from the following aspects:1.A ranking method of interval-valued intuitionistic fuzzy numbers based on distance measurement is proposed.From the perspectives of the score function and the precise function or the formula of the possible degree of the comparison of the interval numbers,the shortcomings or defects of the existing ranking method of the interval-valued intuitionistic fuzzy numbers are discussed.A new distance measure for interval-valued intuitionistic fuzzy sets is defined.Based on the newly defined distance measure,a new sorting method for interval-valued intuitionistic fuzzy numbers is defined,which solves the shortcomings or defects of the existing sorting methods.2.A series of inductive fuzzy entropy theorems for interval-valued intuitionistic fuzzy sets are proposed.The distance between interval numbers is introduced into the definition of fuzziness of interval-valued intuitionistic fuzzy sets and the corresponding property theorems are derived.The proposed definition reflects the nature of fuzziness and is a generalization of the fuzziness of intuitionistic fuzzy sets.The axiomatization definition of interval-valued intuitionistic fuzzy entropy in the existing literatures is modified.Based on the new fuzziness and modified axiomatization definition of fuzzy entropy,a series of induction theorems and a series of entropy formulas of interval-valued intuitionistic fuzzy entropy are proposed.The interval-valued intuitionistic fuzzy entropy formula based on a comprehensive consideration of fuzziness and hesitancy can express both the characteristic information of hesitation and the characteristic information of fuzziness.It is more practical and advantageous in characterization of interval-valued intuitionistic fuzzy sets and has more advantages in solving the problem of interval-valued intuitionistic fuzzy multi-attribute decision making with completely unknown weight by using entropy weight method.3.A multi-attribute group decision algorithm with unknown weights based on interval-valued intuitionistic fuzzy numbers is given,and the feasibility,and effectiveness of the proposed algorithm are verified in the example--Information Management System Selection.