Partial correlation of fuzzy sets

In data analysis and data classification, finding the relationships between the attributes of a database is important. Our objective here is to propose a method of partial correlation analysis on fuzzy sets to investigate the partial relationship between fuzzy attributes. A simple correlation coefficient provides us with a very good sense of linear relationships between fuzzy attribute pairs. But very often, attributes other than the two under consideration are also responsible for the observed association, the effect of these fuzzy attributes may influence the relationship between the observed two fuzzy attributes. It will be more complicated than a simple correlation can explain. Therefore, the analysis of partial correlation is developed here to show the relationship between fuzzy attributes when the effects of other fuzzy attributes are partialed out. Definitions of partial correlation coefficients among fuzzy attributes are derived, and they are defined on the membership grades of the fuzzy attributes. An experiment has been conducted in order to obtain a fuzzy data set and, then, analysis of partial correlation is discussed on this fuzzy data set. (C) 2000 Elsevier Science B.V. All rights reserved.