Enriched Generic Algebras of Fuzzy Relations

The paper presents an overview of a computation friendly calculus of fuzzy relations. It is presented within the framework of an enriched generic algebra of relations that we have been developing since 1979. It is enriched with BK-non-associative products of relations of three kinds: triangle subproduct ⊳, superproduct ⊲ and the square product □. The BK-products have been useful in concise formulation of new theorems in relational mathematics as well as in a number of practical applications in medicine, engineering, information retrieval and elsewhere. The concise algebraic manipulation is also advantageous in symbolic computing. Currently we are engaged in developing an equational theorem checker in which the BK-products play a substantial role. In this endeavour, Tarski style relational calculi play an essential role