Mamdani fuzzy systems for modeling and simulation: A critical assessment

Mamdani systems can incorporate expert knowledge about an input-output relation in the form of IF-THEN rules expressed in natural language. This is a particularly attractive feature for modeling and simulation, but is also one that can be easily misused. Focusing on applied modeling and simulation, this paper discusses why Mamdani systems are not a useful tool to explore the logical consequences of the set of rules used to build them. In the best-case scenario, Mamdani systems provide one of the functions that comply with the specified set of rules, which is a completely different exercise from that of finding the input-output relation implied by the specified set of rules. In general, the logical consequences of a set of IF-THEN rules cannot be captured by a single function. Furthermore, the consequences of including an IF-THEN rule in a Mamdani system can be very different from the consequences of such an inclusion in a system governed by the most basic principles of logical deductive inference. While previous analyses have typically focused on particular steps of the Mamdani process, here we present a holistic approach, explained and illustrated with simple cases and examples.