Abstract
Fuzzy relational equations have been studied in the realm of fuzzy sets for several decades. They have been investigated in the context of fuzzy modeling (fuzzy relational models) and fuzzy control. One interesting look at the relational structures could be established from a perspective of logic relationships (logic expressions) they capture. We consider a fuzzy relational equation in the following form
x circle R = y, (1)
where x and y are fuzzy sets defined in the finite spaces, namely x is an element of [0,1](n), y is an element of [0,1](m) and R is a fuzzy relation defined over the Cartesian product of the corresponding spaces, that is R is an element of [0,1](n) x[0,1](m). The commonly encountered composition operators are those of the max - t and min - s form; here "t" denotes a certain t-norm while "s" stands for a t-conorm.