The concept of fuzzy flip-flop

The authors propose and define a fuzzy flip-flop that is an extended form of an ordinary binary flip-flop, specifically, a J-K flip-flop. A truth table for a J-K flip-flop is fuzzified, extending binary NOT, AND, and OR operations to fuzzy negation, t-norm and s-norm, respectively. Two types of fundamental characteristic equations of the fuzzy flip-flop are introduced: the reset- and the set-type equations, both of which are fuzzy extensions of a characteristic equation of a J-K flip-flop. Their characteristics are demonstrated graphically, especially in the case in which fuzzy negation, t-norm and s-norm relate to complementation, min, and max operations, respectively. Other fundamental fuzzy operations are examined, and their characteristics are demonstrated graphically. Both of the above types are unified in the case of complementation, min, and max operations, and a fundamental characteristic equation for a min-max-type fuzzy flip-flop negation, t-norm and s-norm gates is proposed. A circuit is presented and tested