Ranking Methods Of Intuitionistic Fuzzy Numbers Based On The Risk Attitude

In the wide application of intuitionistic fuzzy numbers, we usually need to compare the pros and cons of the intuitionistic fuzzy numbers. Therefore, the comparison and ranking of intuitionistic fuzzy numbers becomes the focus of research in the field of fuzzy optimization and decision. This paper mainly studies the ranking methods of intuitionistic fuzzy numbers and interval-valued intuitionistic fuzzy numbers, the main contents and achievements are as follows:(1) Considering the decision results are highly affected by the decision maker’s risk attitude, in this paper, we deeply study the composition of the score function which is used to measure the pros and cons of the intuitionistic fuzzy numbers. For the purpose of mirroring decision maker’s mentality, a mentality parameter is introduced. Then, a comprehensive score function is proposed to properly reflect the decision maker’s risk attitude based on the discussion of the membership degree and the non-membership degree. Besides, a new ranking method of intuitionistic fuzzy numbers is given. Furthermore, combined with the intuitionistic fuzzy weighted average operator, a multi-attribute decision method where the criterion weights are given and the criterion values are intuitionistic fuzzy numbers is developed. Finally, an illustrative example is given to demons-trate the effectiveness and feasibility of the multi-attribute decision method.(2) For the pros and cons of the interval-valued intuitionistic fuzzy numbers, firstly, a mentality parameter is introduced in order to reflect the decision maker’s risk attitude in the determination of the membership degree and the non-membership degree and a new score function and an accuracy function are presented. And then the properties of the new score function are discussed. Furthermore, a new ranking method of interval-valued intuitionistic fuzzy numbers is proposed. Secondly, the thesis further discusses the hesitancy information of interval-valued intuitionistic fuzzy numbers, for the purpose of mirroring decision maker’s risk attitude in the tendency of the hesitancy degree, a mentality parameter is introduced. Then, a new score function with three mentality parameters is proposed and a new ranking method is given. Finally, based on the new method, a multi-attribute decision method where the criterion weights are given and the criterion values are interval-valued intuitionistic fuzzy numbers is developed and an illustrative example is given to demonstrate its effectiveness and feasibility.