On Additive and Multiplicative Fuzzy Models

Systems which use a fuzzy rule base and an inference mechanisms are quite frequently used in many applications. Fuzzy rules and inference mechanisms can be described by a system of fuzzy relation equations. A solution to a given system of fuzzy relation equations can serve us a proper model of fuzzy rules (fuzzy model for short). But only two particular solutions, let us call them disjunctive and conjunctive fuzzy models, have been mainly studied so far. The paper aims at new solutions of systems of fuzzy relation equations. The first one additive fuzzy model which is derived from the disjunctive fuzzy model was motivated by several methods often used in practice. The second one — multiplicative fuzzy model — which is derived from the conjunctive fuzzy model was neglected up to now. The paper investigates both new solutions and describes existence of a direct connection between systems of fuzzy relation equations and different fuzzy models. The crucial role of the Ruspini partition is proved and also visually demonstrated.