New Similarity Measures On Interval-Valued Fuzzy Sets

The similarity measures is the research focus of fuzzy set theory,and has been widely used in the fields of group decision-making,fuzzy control,medical diagnosis,pattern recognition,market forecasting and more.In this paper,the similarity measures of type-2 fuzzy sets including intuitionistic fuzzy sets,interval-valued intuitionistic fuzzy sets and Vague sets has been studied systematically.With most similarity measures having the inaccurate classification,inconsistency problems,the following two research work are completed.On the one hand,an improved similarity measure for interval-valued intuitionistic fuzzy sets which based on arithmetic mean is proposed.This measure is a better way to carry forward the idea of arithmetic mean,and show that the interval-valued intuitionistic fuzzy set is a generalization of intuitionistic fuzzy sets better,at the same time,when the upper limits of membership and non-membership are equal to the lower,it can degenerate well into intuitionistic fuzzy,and the range of membership and non-membership in the Cartesian coordinate system can be kept normal.On the other hand,for the intuitionistic fuzzy set,a skewed fuzzy sets is proposed,and its definition and similarity measure are given.This measure takes the "voting model" as an example,proposes that "neutral person have certain ideological tendency,and the ratio of the neutral-pros and neutral-cons is equal to the real proportion of the pros and cons." It construct the distribution of the membership,then a new similarity measure is given based on all of this.This measure explains the problem of neutral people's ideological tendency better.The two similarity measures proposed in this paper all perform well in the public data.The next step is to study the membership distribution of the skewed fuzzy sets and to prove its classification effect could be better.