Ranking Methods Of Intuitionistic Fuzzy Numbers Based On Risk Preference And Geometric Characteristic

Considering membership degree, non-membership degree and hesitancy degree at the same time, intuitionistic fuzzy sets express the fuzzy and uncertain information better, thus having been widely used in the field of fuzzy multiple attribute decision making. The ranking methods of intuitionistic fuzzy numbers and interval-valued intuitionistic fuzzy numbers are important objects in the study of fuzzy multiple attribute decision making, so many researchers pay attention to them. This thesis mainly studies the ranking problems of intuitionistic fuzzy numbers and interval-valued intuitionistic fuzzy numbers. The main achievements are as follows:(1) According to people’s herd mentality and the effect of hesitation on the score of intuitionistic fuzzy number, the hesitation is divided into the membership and non-membership based on its proportion. Thus, new membership degree and non-membership degree of the intuitionistic fuzzy number are ascertained. Besides, taking the risk preference parameter into consideration, the score function is defined by introducing parameter to express decision maker’s risk preference. Furthermore, the corresponding ranking method of intuitionistic fuzzy numbers is given, which is proved to be feasible and effective through examples.(2) According to the geometrical characteristics of intuitionistic fuzzy numbers, the isosceles right triangle that shows intuitionistic fuzzy numbers is split into corresponding blocks. Then, based on the numerical features, which reflect the pros and cons of intuitionistic fuzzy numbers by the sizes of areas of the blocks, the score function and accuracy function of intuitionistic fuzzy numbers are defined. Further, by introducing parameter to express decision maker’s risk preference, the interval-valued intuitionistic fuzzy number is transformed into intuitionistic fuzzy number. Then, based on the geometrical characteristics of interval-valued intuitionistic fuzzy numbers, the definition of the score function and the corresponding ranking method are given. Finally, the feasibility and effectiveness of the method are illustrated.