Extended fuzzy clustering algorithm based on an inclusion concept

Fuzzy modeling of complex systems is a challenging topic. This paper proposes an effective approach to data-based fuzzy optimizing fuzzy system structure and parameters. For this purpose, we cope with fuzzy clustering based on inclusion concept where the rule-base has to be simplified. This simplification occurs in the sense that similar Membership Functions (MF) pertaining to the premise of fuzzy rule-base are merged and replaced by one common MF, capturing the meaning of the former. Reduction of the total number of fuzzy sets improves semantic interpretation and reduces the demand on memory in implementation context. So, we propose an extended algorithm based on the class of fuzzy clustering method and on an inclusion concept proposed by Nefti et al., which is characterized by an inclusion index. During the optimization, the redundant rules are deleted. Finally, interpretability of the fuzzy system is improved. To show the effectiveness of the proposed algorithm, a comparative study of the obtained simulation results with a conventional algorithm based on the class of fuzzy C-means method introduced by Bezdek FCM is presented by a numerical example, which computes a MISO architecture.