Realization of Digital Fuzzy Operations Using Multi-Valued Fredkin Gates

Multi-valued Fredkin gates (MVFG) are reversible gates and they can be considered as modified version of the better known reversible gate the Fredkin gate. Reversible logic gates are circuits that have the same number of inputs and outputs and have one-to-one and onto mapping between vectors of inputs and outputs; thus the vector of input states can be always reconstructed from the vectors of output states. It has been shown that for power not to be dissipated in an arbitrary circuit it is necessary that the circuit be build from reversible gates. Moreover multi-valued Fredkin gates have been shown to be a suitable choice as a basic building block for binary and different alternative logics for example multi-valued logic and threshold logic. In this paper we show the application of MVFGs in the implementation of fuzzy set and logic operations. Fuzzy relations and their composition is very important in this theory as collections of fuzzy if-then rules and, fuzzy GMP (Generalized Modus Ponens)and GMT (Generalized Modus Tollens) respectively is mathematically equivalent to them. In this paper we describe digitized fuzzy sets where the membership values are discretized and represented using ternary variables and the implementation of set operations. The composition of fuzzy relations and a systolic array structure to compute it is described. Design with reversible gates and the highly parallel architecture of systolic arrays makes the proposed circuits quite attractive for implementation.