Discussions on Interpretability of Fuzzy Systems using Simple Examples

Two conflicting goals are often involved in the design of fuzzy rule-based systems: Accuracy maximization and interpretability maximization. A number of approaches have been proposed for finding a fuzzy rule-based system with a good accuracy-interpretability tradeoff. Formulation of the accuracy maximization is usually straightforward in each application area of fuzzy rule-based systems such as classification, regression and forecasting. Formulation of the interpretability maximization, however, is not so easy. This is because various aspects of fuzzy rule-based systems are related to their interpretability. Moreover, user's preference should be taken into account when a single fuzzy rule-based system is to be chosen from several alternatives with different accuracy-interpretability tradeoffs. In this paper, we discuss the difficulty in measuring the interpretability of fuzzy rule-based systems using very simple examples. We do not intend to propose any new interpretability measure. Our intention is to help to activate discussions on how to measure the interpretability of fuzzy rule-based systems. Keywords— Fuzzy systems, fuzzy rules, accuracy-interpretability tradeoff, multiobjective design of fuzzy systems.

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