# Efficient deduction in fuzzy logic

• Roger Martin-Clouaire
Section II Approaches To Uncertainty B) Fuzzy Set Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 286)

## Abstract

The generalized modus ponens is a fuzzy logic pattern of reasoning that permits to make inferences with rules having imprecision both in their antecedent and consequent parts. Though it is a very powerful approximate reasoning tool (from a theoretical point of view), this technique may result in unacceptably slow executions if inappropriately implemented. There are several ways to avoid the inefficiency bottleneck. One of them, that is the object of this paper, consists in introducing an approximation technique focussing only of what is semantically important. This approximation technique is conceived so as to be used in situations where the dependency between two given variables is described via a collection of rules. Moreover, this paper addresses the problem in the setting having the main features that follow:
1. -

the possibility distributions involved in facts and rules are continuous (the referential is the real line), normalized, unimodal and expressed by parametrized functions;

2. -

only single antecedent rules are considered;

3. -

the rules are consistent and it is assumed that their antecedents and consequents do not overlap too much;

4. -

the deduction process is based on the ‘min’ conjunction and Gödel implication operators.

The ultimate goal of this work is to render the generalized modus ponens technique usable in practical deduction systems.

## Keywords

Fuzzy Logic Approximation Technique Possibility Distribution Approximate Reasoning Widening Effect
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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