Fuzzy relational compositions; fuzzy relational products, generalized quantifiers

Fuzzy relational composition has been extensively studied by many authors. We revisit these types of compositions and introduced new definitions that directly employ generalized quantifiers. The motivation for this step is two-fold: first, the application needs for filling a huge gap between the classical existential and universal quantifiers and second, the already existing successful implementation of generalized quantifiers in so called division of fuzzy relations, that constitute a database application counterpart of the theory of fuzzy relational compositions. This paper is an introductory study that should demonstrate a unifying theoretical framework and introduce that the properties typically valid for fuzzy relational compositions are valid also for the generalized ones, yet sometimes in a weaken form.