PROBABILISTIC SETS AND FUZZY-REASONING TO BUILD RELATION BETWEEN SUBJECTIVE AND OBJECTIVE VARIABLES SETS

This paper presents a new approach for getting into relation two data sets: the first one having a subjective origin and the second one bein g objective. The purpose of this paper is not to compete with improved data analysis methods, but to propose, if data can be taken into acco unt as probabilistic fuzzy sets, to use fuzzy reasoning in order to ge t into relation the two data sets. First, the two probabilistic fuzzy sets coming from the raw data are built when considering complementary cumulative distribution functions. Then, fuzzy reasoning on inference rules is considered. It leads to linking the two obtained distributio n functions through a conditional possibility measure. In order to fit the generalized modus ponens, a composition operator has to be consid ered too. Then, having a possibility measure-composition operator pair , its ability to be applied on a given data sample is assessed through performance indexes. The performances of 19 pairs are compared to get two sets of fictitious data into relation. The results are compared w ith those of the statistical method of principal component analysis.