Recently evolutionary multiobjective optimization (EMO) algorithms have been actively used for the design of accurate and interpretable fuzzy rule-based systems. This research area is often referred to as multiobjective genetic fuzzy systems where EMO algorithms are used to search for a number of non-dominated fuzzy rule-based systems with respect to their accuracy and interpretability. The main advantage of the use of EMO algorithms for fuzzy system design over single-objective optimizers is that multiple alternative fuzzy rule-based systems with different accuracy-interpretability tradeoffs are obtained by their single run. The decision maker can choose a single fuzzy rule-based system according to their preference. There still exist several important issues to be discussed in this research area such as the definition of interpretability, the formulation of interpretability measures, the visualization of tradeoff relations, and the interpretability of the explanation of fuzzy reasoning results. In this paper, we discuss the ability of EMO algorithms as multiobjective optimizers to search for Pareto optimal or near Pareto optimal fuzzy rule-based systems. More specifically, we examine whether EMO algorithms can find non-dominated fuzzy rule-based systems that approximate the entire Pareto fronts of multiobjective fuzzy system design problems.