Area-based Vague Entropy And Its Application In Cluster Analysis

In recent years,with the progress of information systems,the fuzzy entropy of vague sets and the research in cluster analysis have been highly concerned by scholars at home and abroad.In 1993,Gau and Buehrer proposed the theory of dealing with fuzzy information-vague set theory,which is essentially an extension of fuzzy set theory.Based on the existing fuzzy entropy of several vague sets,especially the idea of distance-based fuzzy entropy,this paper proposes an improved fuzzy set entropy of vague sets based on the axiomatized definition of fuzzy entropy and the understanding of constraint conditions for vague sets.through the proof of the improved Vague entropy method and the analysis of the experimental data,this paper discusses the problems of different Vague entropy's ability of distinguishing different data and the degree of vagueness.Based on this,the improved vague entropy is applied to the cluster analysis.The analysis of specific examples gives reasonable results.The main contents are as follows:Firstly,this paper introduces the related theories of Vague sets,fuzzy entropy and clustering analysis,namely the definition,operation and properties of vague sets.According to the axiomatic definition and constraint conditions of fuzzy entropy of vague sets,this paper analyzes several vague set methods of fuzzy entropy.Secondly,aiming at the shortcomings of existing fuzzy entropy for the lack of distinguishing ability of different data,extending distance characterization vague entropy to area metrics,a new area-based vague entropy is proposed and generalized to n-dimensional space,its completeness is proved in theory.The comparative analysis of examples shows that the new entropy formula solves the disadvantage better that distance-based vague entropy cannot intuitively reflect its degree of blurring,and has good validity and rationality.Finally,due to the uncertainty of clustering analysis,the combination of Vague set theory and clustering analysis makes the solution of clustering analysis more reasonable and effective.In this paper,the improved area-based Vague entropy similarity measure is chosen as the basis for establishing similarity matrix in cluster analysis problem.By analyzing the clustering analysis algorithm based on Vague set theory,it is known that constructing similar matrix is an important process.Directly affecting the subsequent classification results,the improved Vague entropy proposed in this paper is applied to the construction of similar metrics of traditional clustering and Q-clustering and applied to pattern recognition and other specific examples.The clustering based on area Vague entropy is obtained by comparison.Analysis can obtain reasonable and effective classification results more than traditional clustering,Q-clustering and pattern recognition.