Cluster Analysis And Forecasting Based On Fuzzy Set-valued Statistics

Clustering analysis, which is a classification method of samples or indexes is an important and practical technical in multivariate statistics. The so-called "class", popularly speaking, is a set composed by similar elements. The factors (indexes) are always determined in clustering analysis of multivariate statistical. But in the actual problem, we often meet the condition that factors (indexes) are not certain, and they are fuzzy. Clustering analysis of multivariate statistics are not suit to solve these problems. In this paper we study the analytical method of fuzzy set-value statistical as these factors (indexes) are fuzzy numbers.First, the fuzzy diatance and the similarity coefficient of two fuzzy numbers are introduced, then clustering method of fuzzy set-valued statistical is studied. The solution method and process of system clustering method are presented at length. Some simple properties and the determination of classes are also given.Based on structured element, a new definition of fuzzy distance between two fuzzy sets is proposed. The new definition of fuzzy distance overcomes the defect as the value is real number. The approach to obtain the membership degree is proposed. Prediction method based on fuzzy set-valued statistics is presented. Particularly, the prediction method in the condition that fuzzy value is reduced into interval-valued is given, which is more suitable in fuzzy synthetic decision and fuzzy search. Finally, the pediction method when the statistics is general fuzzy numbers is simply presented.