Type-2 fuzzy systems have been investigated as an alternative formalism to deal with uncertainty when the classic Type-1 fuzzy systems do not offer the suitable flexibility for the representation of the information being modeled. The higher flexibility in representation comes with a higher complexity in the system modeling, mainly in the design of the Type-2 fuzzy sets and in the definition of the inference engine parameters. In this paper, we focus on the Type-2 fuzzy systems design, proposing a multi-objective evolutionary approach for tuning the Type-2 inference engine of a fuzzy rule-based classification system by means of automatically choosing the t-norm used in the inference process. The selection of the t-norm used plays an important hole, since different operators could lead to different results. In a preliminary version of this work, we have proposed an approach to design and optimize Type-2 fuzzy systems that includes the tuning of Type-2 fuzzy sets and the selection of rules. The additional tuning process proposed in this paper is an extension of the previous method in the sense that the same evolutionary procedure performs simultaneously the tuning of the inference mechanism and the tasks performed before. The evolutionary process is executed by means of a multi-objective genetic algorithm with three objectives that aim to balance the accuracy and interpretability of the system generated: the accuracy, the number of rules and the number of conditions in the rules. The proposed method has been compared with a state-of-the-art method proposed in the literature, presenting good results.
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