Probabilistic sets and fuzzy reasoning for data analysis problems

Abstract This paper presents two methods based on probabilistic sets to achieve some problems in data analysis. We are indebted to Professor Arnold Kaufmann for the beginnings of these two methods; some of the first ideas were found in his prolific work. The first method is related to subjective data analysis, the second one is an approach for establishing a relationship two data sets, the first one having a subjective origin and the second one being objective. The purpose of this paper is not to compete with improved data analysis methods but to propose, if data can be taken into account as probabilistic fuzzy sets, to use such a representation, which loses very little information. Both methods were tested on real data and the results compared with those obtained with improved data analysis methods, mainly those of the Principal Component Analysis and Multiple Correspondence Factor Analysis.