An ordinal framework for data mining of fuzzy rules

The benefit of computing with linguistic terms is now generally accepted. The processing of linguistic concepts and expressions is made possible mainly by fuzzy set theory. It constitutes a quantification of the compatibility degree of objects with the associated linguistic concept using a membership function. When fuzzy sets are combined by intersection in the evaluation of fuzzy rules, the implicit assumptions are that the membership values have quantitative semantics and that the numeric values are commensurable among the different fuzzy sets generated by the concepts involved. In most situations these assumptions are not justified. It is more suitable to interpret membership values as numeric representations of compatibility orderings. In this paper, we propose the concept of ordinal fuzzy set as basis for interpretation of fuzzy rules. This frees us from the implicit assumptions mentioned and avoids some of the anomalies these assumptions produce