New mixed-coding PSO algorithm for a self-adaptive and automatic learning of Mamdani fuzzy rules

Abstract

Thanks to its algorithmic performances, PSO algorithm becomes a popular tune tool for fuzzy systems in literature. However, it still encounters many complications, especially when dealing with Mamdani fuzzy system type because of its nature. The Mamdani fuzzy system is known as a linguistic model where the semantic meaning of the fuzzy rules is an intrinsic characteristic that must be retained during the learning process, while seeking for high accuracy. Therefore, to tune the Mamdani fuzzy system, it is very crucial to well represent each rule in a way that preserves this characteristic firstly, and to look for a search mechanism to optimize them throughout this topic secondly. In this paper, we introduce a new and promising approach to optimize the Mamdani fuzzy systems without a need of any prior knowledge. To the best of our knowledge, this approach is the first to optimize simultaneously the membership functions, the scaling factor parameters and the fuzzy rule conclusions with a mixed-coding PSO algorithm by combining a special monitoring function and a self-adaptive threshold. The proposed approach is validated by a comparative study with other design strategies taken from Box–Jenkinsgas furnace system literature and two theoretical examples in addition to a real-time control of the inverted pendulum Feedback 33-200. The obtained results proved the potential and the effectiveness of the proposed approach.