Some considerations about a least squares model for fuzzy rules of inference

Abstract

In this paper, the method of least squares is applied to the fuzzy inference rules. We begin studying the conditions in which from a fuzzy set we can build another through the method of least squares. Then we apply this technique in order to evaluate the conclusions of the generalized modus ponens and the generalized modus tollens. We present different theorems and examples that demonstrate the fundamental advantages of the method studied. We conclude presenting a method for obtaining the conclusion when working with fuzzy conditional propositions that contain two fuzzy propositions joined by the connective “and”.