A MATHEMATICAL-THEORY OF SYSTEM FLUCTUATIONS USING FUZZY MAPPING

In the direct product space of a complete metric linear space X and it s related space Y, a fuzzy mapping G is introduced as an operator by w hich we can define a projective fuzzy set G (x, y) for any x is-an-ele ment-of X and y E is-an-element-of Y. An original system is represente d by a completely continuous operator f (x) is-an-element-of Y, e.g., in the form x = lambda(f (x)), (lambda is a ljnear operator), and a no ndeterministic or fuzzy fluctuation induced into the original system i s represented by a generalized form of system equation x is-an-element -of (beta)G (x,f (x)). By establishing a new fixed point theorem for t he fuzzy mapping G, the existence and evaluation problems of solution are discussed for this generalized equation. The analysis developed he re for the fluctuation problem goes beyond the scope of the perturbati on theory.