Abstract
Fuzzy logic presents many potential applications for modelling and simulation. In particular, this paper analyses one of the most popular fuzzy logic techniques: Mamdani systems. Mamdani systems can look particularly appealing because they are designed to incorporate expert knowledge in the form of IF-THEN rules expressed in natural language. While this is an attractive feature for modelling and simulating social and other complex systems, its actual application presents important caveats. This paper studies the potential use of Mamdani systems to explore the logical consequences of a model based on IF-THEN rules via simulation. We show that in the best-case scenario a Mamdani system provides a function that complies with its generating set of IF-THEN rules, which is a different exercise from that of finding the relation or consequences implied by those rules. In general, the logical consequences of a set of rules cannot be captured by a single function. Furthermore, the consequences of an IF-THEN rule in a Mamdani system can be very different from the consequences of that same rule in a system governed by the most basic principles of logical deductive inference. Thus, care must be taken when applying this tool to study “the consequences†of a set of hypothesis. Previous analyses have typically focused on particular steps of the Mamdani process, while here we present a holistic assessment of this technique for (deductive) simulation purposes.
Highlights
IntroductionThe theory of fuzzy sets has been successfully applied in a wide range of fields, but – contrary to its creator’s initial expectations – most applications are found outside the boundaries of the Social Sciences
The use of fuzzy set theory in the Social Sciences is certainly not widespread, but ever since the early pioneering proposals there has been a constant interest in potential applications of fuzzy logic for social modelling and simulation (Arfi ; Ragin & Pennings )
A wide range of computer tools have been developed over the past years to make use of fuzzy logic in modelling, simulation and decision making, and many general computing environments such as MatLab implement popular fuzzy methods, like the so-called “Mamdani fuzzy inference” (MATLAB )
Summary
The theory of fuzzy sets has been successfully applied in a wide range of fields, but – contrary to its creator’s initial expectations – most applications are found outside the boundaries of the Social Sciences. . The use of fuzzy set theory in the Social Sciences is certainly not widespread, but ever since the early pioneering proposals (see e.g. Cio i-Revilla ; Smithson ) there has been a constant interest in potential applications of fuzzy logic for social modelling and simulation (Arfi ; Ragin & Pennings ). A wide range of computer tools have been developed over the past years to make use of fuzzy logic in modelling, simulation and decision making, and many general computing environments such as MatLab implement popular fuzzy methods, like the so-called “Mamdani fuzzy inference” (MATLAB )
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