Fuzzy logic controllers using generalized operators defined on the basis of certainty function

In this paper new generalized operators, based on a fuzzy entropy approach are presented. After a general discussion on fuzzy entropy the concept of elementary certainty function of a fuzzy set is introduced. Using this mapping, the generalized intersections and unions are defined as mappings, that assign the less and the more certain membership grade to each of the elements of the domain of the operators, respectively. It is shown that these operators satisfy the axiom system of generalized operations and can be constructed from the conventional min and max operations. The second part of the paper investigates the applicability of the new operators in fuzzy logic controllers. Simulations have been carried out so as to determine the effects of the operators on the performance of the fuzzy controllers