Fuzzy reasoning based on generalized fuzzy if-then rules

This paper focuses on a fuzzy reasoning method based on a generalized If-Then rule. Firstly, the antecedent and the consequent of an If-Then rule are considered and expressed as a component of a kind of binary L-type fuzzy relation on the product of the universes of discourse and the range of definition for a certain fuzzy attribute. Then a generalized extension principle based on this L-type fuzzy relation (FR-GEP) is constructed. Moreover, the paper gives a detailed description of this generalized If-Then rule using 20 well-known common implication operators in the framework of the composition of L-type fuzzy relations. Consequently, an L-type binary fuzzy reasoning method based on this generalized If-Then rule is established according to FR-GEP.