Research On The Similarity And Application Of Bipolar Fuzzy Sets

Wen-Ran Zhang put forward the concept of Bipolar fuzzy sets in 1994,so as to deal with the uncertainty and bipolarity of information.The bipolar fuzzy sets interprets or describes the inherent polarity of objective things well.It has been attracted much attention,and some scholars at home and abroad have made more in-depth research on the theory of bipolar fuzzy sets,and have obtained great research results.Similarity is an important method to measure the degree of similarity between two fuzzy sets.It is a very important research content in fuzzy set theory and its applications.Bipolar fuzzy sets are a new extended form of fuzzy sets.It has more advantages than fuzzy sets in the processing of bipolar value of information,but the research on similarity of bipolar fuzzy sets is still in the exploratory stage,and the application field needs to be further developed.Therefore,this paper studies the similarity of two bipolar-value fuzzy sets and the main accomplishments of the paper are as follows:First,the distance measure of bipolar fuzzy set is defined,and based on the Hamming distance,Euclidean distance,Hausdorff distance and a series of distance measures of the bipolar fuzzy set are extended,including standard distance measurement,continuous distance measurement,weighted distance measurement and the corresponding properties are proved,and then the rationality of the proposed distance formula is verified through calculation examples.Secondly,Based on the newly defined distance measure,the definition of similarity of bipolar fuzzy sets is given,and the similarity of four bipolar fuzzy sets are constructed from the perspective of distance measurement,set operation,arithmetic mean value,and cosine similarity.The formula also gives the properties of the similarity of these four bipolar fuzzy sets.Finally,an practical analysis is given on the application of the similarity of the four bipolar fuzzy sets are proposed in this paper in mode recognition and multi-attribute decisionmaking problem.