Classivalent and difunctional relations in the interval calculus of fuzzy BK-products

The paper presents theorems characterizing classivalent relations based on t-norm residuated fuzzy logics. The classivalency conditions are characterised by various relational inequalities containing the BK-products of relations. This generalizes to the realm of t-norm resuduated fuzzy logics the characterization of classivalency by means of square products of relations previously given by Bandler and Kohout (1977). The proofs of the most important theorems are conducted rigorously in the first order predicate fuzzy logic BL that was developed by P. Hajek (1998). The paper concludes with the extensions of characterisation of classivalency to the relations based on the checklist paradigm based fuzzy interval logics of Bandler and Kohout. There are five families of such logics, but the paper restricts the discussion to the systems generated by measure m₁. It should be noted that difunctional relations are a special case of the classivalent relation, namely total classivalent relations. Thus classivalency could also be called partial difunctionality