How far can we go with fuzzy logic? Perspectives on model-based reasoning and stochastic resonance in scientific models SILVIA DE BIANCHI ∗ and SILVIA GAUDENZI † , University of Rome ‘La Sapienza’, Italy Abstract Despite the success of fuzzy systems in applications to heuristic controls, fuzzy function approximators behave like a mathematical model endowed of a fundamental regulative role, but of an intrinsically provisional and non-explanatory nature. We shall therefore discuss strengths and weaknesses of fuzzy logic applications to stochastic resonance models and expound the epistemological questions emerging therein. Keywords: Fuzzy logic, stochastic resonance models, adaptive stochastic resonance, fuzzy learning law. 1 Introduction In this article, we shall investigate the epistemological implication of the use of fuzzy logic in specific stochastic resonance (SR) models. SR models are grounded in the interplay of non-adiabatic transitions between two frequencies that experience a shift or a switch due to an excitation. It appears that a fuzzy function approximator perfectly adheres to SR models in shaping an empirical law that allows taking control over the outputs and calculating the behaviour of the system. The debate on fuzzy logic and its status is vast and increased insofar as its application to heuristic controllers is successful and leads to reliable results. 1 To shed light on strengths and limitations of fuzzy logic, we shall emphasize that fuzzy logic-based models behave like mathematical models, but they can be substituted by mathematical models that embody the physical laws of a system. In fact, fuzzy logic is an effective tool when the dynamics of a system is not given and cannot be described or grasped by a mathematical model. It is one of the tools that scientists use in taking control of the outputs of a system, by manipulating variables and giving rise to an ensemble of fuzzy rules, which have an empirical nature. The successful use of fuzzy logic generally implies a weakness or insufficiency of mathematical models and a lack of knowledge of the physical laws governing complex non-linear systems. These aspects disclose a valuable source for epistemological questions: (i) Fuzzy-logic-based control systems, even though successfully used in many branches of physics and engineering, have no explanatory function per se and therefore exclude the explanation or causal account of complex systems. The latter can be reached by integrating these systems within another mathematical model that sometimes cannot be available. (ii) The relationship between mathematical models and physical reality is assumed to be an approximation; deductive reasoning and bivalent logic are insufficient in scientific practices and must be supplied with other kinds of reasoning; however, the use of fuzzy-logic-based models admits the possibility of accounting for a system on ∗ E-mail: silvia.debianchi@uniroma1.it † E-mail: silvia.gaudenzi@roma1.infn.it 1 For an overview of the debate see references [20, 29, 30]. Vol. 21 No. 6, © The Author 2013. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com doi:10.1093/jigpal/jzt007 Advance Access published 1 April 2013 Downloaded from https://academic.oup.com/jigpal/article-abstract/21/6/1044/716498 by Universitat Autònoma de Barcelona user on 06 June 2018