Extensions of fuzzy relational compositions based on generalized quantifiers

The aim of this paper is to extend the fuzzy relational compositions motivated by their applications to medical diagnosis problem by Bandler and Kohout. These compositions employ two quantifiers, the universal quantifier and the existential quantifier. As there exists a big gap between these two quantifiers, that may be appropriately filled in by intermediate generalized quantifiers, we take this as a motivation for our study. In particular, we introduce the concept of fuzzy relational compositions based on generalized quantifiers. Furthermore, we show that the properties that are typically valid for standard fuzzy relational compositions are also valid for the compositions based on generalized quantifiers, yet sometimes in a weaken form. Apart from fuzzy relational compositions, the use of generalized quantifiers is also applied to images and preimages of fuzzy sets under fuzzy relations.