Generalized Implicative Model of a Fuzzy Rule Base and its Properties

In this contribution, an implicative variant of the conjunctive normal form will be recalled and further studied. This normal form is an alternative to the Perfilieva’s conjunctive normal form. It will be shown that it is a suitable model for a particular case of graded fuzzy rules introduced as a generalization of classical fuzzy rules. Moreover, approximation properties of the implicative variant of the conjunctive normal form provide a view on a class of fuzzy relations that can be “efficiently” approximated using this normal form. Newly, a suitable inference rule the graded rules formalized using the implicative variant of the conjunctive normal form will be introduced and analyzed. Results in this field extend the theory of approximate reasoning as well as the theory of fuzzy functions. Keywords-Graded fuzzy rules; Normal forms; Approximate reasoning; Fuzzy functions; Fuzzy control;