The Ranking Of Fuzzy Numbers Based On The Relative Superiority Degree

People’s judgements are often fuzzy and uncertain in practical life. The fuzzy uncertainty characteristics are usually described by fuzzy numbers in the theory of fuzzy sets. Therefore, the comparison and ranking of fuzzy numbers are the key subjects in the field of fuzzy optimization and fuzzy multi-attribute decision making, which has been made a lot of research by many domestic and foreign scholars. In this thesis, based on the relative superiority degree, fuzzy comparison and ranking is mainly studied. The main contents and results are listed as follows:(1) From the standpoint of view on benefit of comparison and ranking, differences of two interval numbers corresponding points are moderately enlarged by s function. Then a new definition is given for the relative superiority of interval numbers. The relative superiority matrix is obtained by the binary comparison for a set of given interval numbers and the fuzzy complementary judgment matrix is constructed. Thus, a new method of ranking of interval numbers is presented based on relative superiority. Combined with UWA operator, the method is proposed for multiple attribute decision making, whose attribute values are interval numbers. Meanwhile, its feasibility and practicality is demonstrated by an example.(2) The relative superiority of intuitionistic fuzzy numbers is defined based on relative superiority of interval numbers. According to relative superiority matrix for the binary comparison of intuitionistic fuzzy numbers, the fuzzy relative judgment matrix is given. Then a ranking method of intuitionistic fuzzy numbers is presented on the basis of relative superiority. Combined with IFWG operator, a multiple attribute decision making method is proposed, in which attribute values are intuitionistic fuzzy numbers and the weights are real numbe-rs. Finally, an illustrative example is given to show its validity and practicality.(3) According to the membership interval and non-membership interval of interval-valued intuitionistic fuzzy numbers, the relative superiority of interval numbers is extended to the relative superiority of interval-valued intuitionistic fuzzy numbers. Based on relative superiority matrix for the binary comparison of interval-valued intuitionistic fuzzy numbers, the fuzzy relative judgment matrix is given. Then a ranking method of interval-valued intuitionistic fuzzy numbers is presented on the basis of relative superiority. Combined with IIFWA operator, a multiple attribute decision making method is proposed, in which attribute values are interval-valued intuitionistic fuzzy numbers and the weights are real numbers. Finally, an illustrative example is given to show its rationality and practicality.