Parameterized uninorm and absorbing norm and their application for logic design

The paper deals with the properties of the system of uninorm and absorbing norm, and their application for logic design. In particular, the norms are specified by the use of a novel symmetric generating function, and are considered as operators of a non-distributive algebraic system. It is demonstrated that from the logical point of view, the absorbing norm provides a novel fuzzy negated xor operator, while the uninorm provides both fuzzy and and or operators, and determines fuzzy not operator. On the basis of the considered properties of the norms, the fuzzy T-flip-flop and JK-flip-flop are defined and their actions are demonstrated.