Application of fuzzy implication to probe nonsymmetric relations: Part I

Abstract Nine fuzzy implication operators were studied to determine their ability to identify nonsymmetric relations. The fuzzy degrees of the antecedent and consequent propositions of each implication were evaluated using the cumulative distribution function, which has the property that fuzzy degrees are uniformly distributed between 0 and 1 and hence are as fuzzy as possible. Under these conditions, average implications from the nine operators are confined to small subintervals of [0, 1]. For eight out of nine implication operators, the average implication largely duplicates information from the correlation coefficient. These points are explained theoretically. Confidence limits for fuzzy implication are also discussed.