Complexity, interpretability and explanation capability of fuzzy rule-based classifiers

Recently fuzzy system design has been frequently formulated as multiobjective optimization problems with two conflicting goals: maximization of accuracy and interpretability. Whereas the formulation of accuracy maximization is usually straightforward in each application task, it is not easy to define the interpretability of fuzzy rule-based systems. As a result, interpretability maximization is often handled as complexity minimization. In this paper, we discuss whether the complexity minimization leads to the interpretability maximization in the design of fuzzy rule-based systems for pattern classification problems. Using very simple artificial test problems, we show that the complexity minimization does not always lead to the interpretability maximization. We also discuss the explanation capability of fuzzy rule-based systems to explain their reasoning results to human users in an understandable manner. We show that the interpretability maximization is closely related to but different from the explanation capability maximization.