Mamdani Fuzzy Systems for Modelling and Simulation: A Critical Assessment

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.