Algebraic fuzzy flip-flop circuits

Algebraic fuzzy flip-flop circuits in discrete and continuous mode are presented. The algebraic fuzzy flip-flop is one example of the general fuzzy flip-flop concept which has been defined as an extension of the binary J-K flip-flop. Two types of the algebraic fuzzy flip-flop, which are reset type and set type, are defined using complementation, algebraic product, and algebraic sum operations for fuzzy negation, t-norm, and s-norm, respectively. A unified equation of the reset type and set type of an algebraic fuzzy flip-flop is derived for the purpose of realization of hardware circuits. Based on the equation, two types of hardware circuits, in discrete mode and continuous mode, are constructed. Moreover the characteristics of various fuzzy flip-flops presented previously are investigated such as min-max fuzzy flip-flop in both discrete and continuous mode, and the algebraic fuzzy flip-flop presented in this paper.