Fuzzy Implications and Some Functional Equations

Abstract

Generally speaking functional equations are equations in which the unknowns are functions. In the previous chapters we have seen some functional equations, viz., the exchange property (EP), the contrapositive symmetry (CP) and the like. But as Prof. Aczél writes in his book [1] “merely stating properties (functional equations) satisfied by a function is different from solving and determining all functions that satisfy a given functional equation”.

In this chapter we deal with a few functional equations involving fuzzy implications. These equations, once again, arise as the generalizations of the corresponding tautologies in classical logic involving boolean implications.