Abstract
In this paper we consider the transformation of the polynomial form of generalized composite fuzzy relational equation into the equivalent monomial form in order to loosen substantially the severe difficulty in solving the polynomial form of generalized composite fuzzy relational equation for the unknown fuzzy relation.
First, we assume the generalized binary operation * on the range space of the membership function, _??__??_{u|0≤u≤1}.
Second, the generalized composition of two fuzzy relations is defined by applying an arbitrary ordered pair of two generalized binary operations on _??_.
Third, we show the necessary and sufficient condition for the transformability of the polynomial form into the equivalent monomial form. Furthermore, it is concluded that the transformability is guaranteed, if an algebraic structure of the range space _??_ is a commutative semi-ring.
Finally, we present some examples of the algebraic structure which guarantees the transformability of the polynomial form into the equivalent monomial form.
