How to Gauge the Accuracy of Fuzzy Control Recommendations: A Simple Idea

Fuzzy control is based on approximate expert information, so its recommendations are also approximate. However, the traditional fuzzy control algorithms do not tell us how accurate are these recommendations. In contrast, for the probabilistic uncertainty, there is a natural measure of accuracy: namely, the standard deviation. In this paper, we show how to extend this idea from the probabilistic to fuzzy uncertainty and thus, to come up with a reasonable way to gauge the accuracy of fuzzy control recommendations. 1 Formulation of the Problem Need to gauge accuracy of fuzzy recommendations. Fuzzy logic (see, e.g., [1, 4, 6]) has been successfully applied to many different application areas. For example, in control – one of the main applications of fuzzy techniques – fuzzy techniques enable us to generate the control value appropriate for a given situation. A natural question is: with what accuracy do we need to implement this recommendation? In many applications, this is an important question: it is often much easier to implement the control value approximately, by using a simple approximate actuator, but maybe a more accurate actuator is needed? To answer this question, we must have a natural way to gauge the accuracy of the corresponding recommendations. Patricia Melin and Oscar Castillo Department of Computer Science, Tijuana Institute of Technology, Tijuana, Baja California, Mexico, e-mail: [email protected], [email protected] Andrzej Pownuk, Olga Kosheleva, and Vladik Kreinovich University of Texas at El Paso, 500 W. University, El Paso, Texas 79968, USA, e-mail: [email protected], [email protected], [email protected]