Formal Validation of Fuzzy Control Techniques. Perspectives

In this paper, a survey of the state of the art and perspectives of two main lines of research in fuzzy control systems is presented: on one hand, the \emph{interpolative-functional line} representing fuzzy systems as parameterized universal function approximators, thus applying nonlinear control and neural network paradigms; on the other hand, a \emph{logic-formal} approach where fuzzy systems are analysed in terms of logic interpretations, exploring validation, consistency and completeness, uncertainty management and knowledge supervision. The former approach is not widely used in the control field, and asserting its possibilities is one of the main motivations of this paper. References in both lines and some abridged results in the second case are cited, in particular some of the author's contributions, to which the interested reader is referred.