Fuzzy systems evaluation: The inference error approach

An inference method based on an equation image of a rule-base and the minimization of a cost index (inference error) is presented. The method has several advantages: it has intuitive insight, allows more powerful rules, and also presents an interesting algebraic (minimum distance) and functional (subsethood) formulation of the meaning of inference. Analysis of internal quality and completeness of a fuzzy rule-base and validity checks of inference methods can be expressed as numeric indexes. This is applied to logical verification of common structures widely used in PID fuzzy controllers.