Fuzzy Logic and Education: Teaching the Basics of Fuzzy Logic through an Example (by Way of Cycling)

Abstract

Fuzzy logic dates back to 1965 and it is related not only to current areas of knowledge, such as Control Theory and Computer Science, but also to traditional ones, such as Philosophy and Linguistics. Like any logic, fuzzy logic is concerned with argumentation, but unlike other modalities, which focus on the crisp reasoning of Mathematics, it deals with common sense reasoning; i.e., with approximate reasoning. Although the teaching of logic has formed part of mainstream education for many years, fuzzy logic is a much more recent inclusion. In this paper we emphasize the desirability of having illustrative examples related to students’ everyday activities, such as sports, in order to introduce fuzzy logic in higher education. Taking an example from cycling, we show, step by step, how to model an approximate reasoning regarding the choice of a ratio (a combination of freewheel and chainring) in order to advance more or less with each rotation of the pedals. Led by this example, a number of alternatives attending to the formal representation of the premises and the ways of inferring a plausible conclusion are analyzed. The choices made between alternatives are justified. We show that the conclusion inferred in the example is consistent with the models selected for premises and fuzzy inference and similar to that concluded by a human being