In the design of fuzzy rule-based systems, we have two conflicting goals: One is accuracy maximization, and the other is complexity minimization (i.e., interpretability maximization). There exists a tradeoff relation between these two goals. That is, we cannot simultaneously achieve accuracy maximization and complexity minimization. Various approaches have been proposed to find accurate and interpretable fuzzy rule-based systems. In some approaches, these two goals are integrated into a single objective function which can be optimized by standard single-objective optimization techniques. In other approaches, accuracy maximization and complexity minimization are handled as different objectives in the framework of multiobjective optimization. Recently, multiobjective genetic algorithms have been used to search for a large number of non-dominated fuzzy rule-based systems along the accuracy-complexity tradeoff surface in some studies. These studies are often referred to as multiobjective genetic fuzzy systems. In this chapter, we first briefly explain the concept of accuracy-complexity tradeoff in the design of fuzzy rule-based systems. Next we explain various studies in multiobjective genetic fuzzy systems. Two basic ideas are explained in detail through computational experiments. Then we review a wide range of studies related to multiobjective genetic fuzzy systems. Finally we point out future research directions.
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