Optimality Degree Measurement in Fuzzy System Interfaces

In this paper we propose an extension of the optimality condition for fuzzy system interfaces. Specifically, the classical optimality condition is modified so as to provide a degree of optimality ranging from zero to one, the latter corresponding to optimal fuzzy interfaces in the classical sense. Optimality degree is defined both punctually and globally, where global optimality degree is derived by integrating punctual degrees over all the input domain. The optimality degree measurement is particularly useful for Output Interfaces, generally implemented by means of defuzzification algorithms, which seldom satisfy the optimality condition. Indeed, it can be used to compare different defuzzification strategies, so as to choose that with maximal optimality degree. Moreover, its punctual representation can be exploited to devise hybrid defuzzification strategies that locally maximize optimality degrees. In this work, optimality degree is applied to Mamdani Fuzzy Inference Systems with several defuzzification strategies to highlight quality variations attained by different Output Interfaces