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Fuzzy inference using a least square model.

Humberto BustinceM. CalderónVictoria Mohedano — 1998

Mathware and Soft Computing

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. We present different theorems and examples that demonstrate the fundamental advantages of the method studied.

Method of least squares applied to the generalized modus ponens with interval-valued fuzzy sets.

Eduard AgustenchHumberto BustinceVictoria Mohedano — 1999

Mathware and Soft Computing

Firstly we present a geometric interpretation of interval-valued fuzzy sets. Secondly, we apply the method of least squares to the fuzzy inference rules when working with these sets. We begin approximating the lower and upper extremes of the membership intervals to axb type functions by means of the method of least squares. Then we analyze a technique for evaluating the conclusion of the generalized modus ponens and we verify the fulfillment of Fukami and alumni axioms [9].

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