Approximate Inclusion Between Fuzzy Sets - Application to the Division of Fuzzy Relations

This paper is devoted to an extension of the inclusion operator. The regular inclusion of A in B entails that any element of A is also a member of B. The idea suggested in this paper is to soften the universal quantifier (all) into "almost all". It is shown that diverse approaches to the relaxation can be envisaged in order to design an approximate inclusion whose result is either Boolean, or valued in the unit interval. A concrete usage of this type of inclusion is illustrated in the area of databases, with the approximate division of relations