Improvement And Application Of Vague Set Similarity Measure Under The Influence Of Abstention

In recent years,the similarity measure of Vague sets and the method of multi-attribute decision based on Vague sets have been paid much attention by scholars.In 1993,Gau and Buehrer put forward the theory of Vague set which can deal with fuzzy information and the essence of this theory is the extension of Fuzzy set theory.In this paper,we consider the idea of similarity measure based on several Vague sets and take into account the influence of the abstention on the similarity measure of Vague sets.Through the proof of the improved similarity measure and the analysis of the experimental data,the influence of the improved similarity measure method on the data differentiation is discussed.On the basis of this,the improved similarity measure method is applied to multi-attribute decision,and the result of the example is reasonable.The contents of this paper are mainly arranged as follows.Firstly,the definition and properties of the similarity measure of Vague sets are introduced.The conditions and theorems of the constructing similarity measure method are analyzed.The existing similarity measure method does not take into account the abstention part of the impact,and the data cannot be effectively distinguished.Therefore,an improved similarity measure method and an improved weighted similarity measure method are proposed.The definition completeness of the improved similarity measure method is proved in theory,and the effect of this method on the data is analyzed by random experimental data.In order to further expand the scope of the data,respectively,the paper takes 36*36 group data in steps of 0.1 and 2602*2602 data in steps of 0.01 which interval on [0,1].By analyzing and comparing several measurements,it is concluded that the improved measurement method is more effective and more efficient for data differentiation.Secondly,Vague set theory can make the problem solution of multi-attribute decision more efficient and effective.Based on Vague set theory,the steps of multi-attribute decision algorithm are analyzed,and the alternative ranking is an important factor that affects the decision results.In order to reasonably distinguish between alternatives,this paper selects the ranking function similarity formula as multiple attribute decision problems with the improved Vague set.Finally,the improved similarity measure of Vague set is applied to the simple weighting method,TOPSIS method and dynamic information aggregation method,and the results are reasonable.