On a Qualitiative Approximate Inclusion -- Application to the Division of Fuzzy Relations

This paper is devoted to an extension of the inclusion operator. The logical view of the inclusion between fuzzy sets rests on the use of fuzzy implications. The idea suggested in this paper is to relax R-implications in order to tolerate low-level intensity exceptions and thus obtain a qualitative approximate inclusion. A concrete usage of this type of inclusion is illustrated in the area of databases, with the approximate division of relations