Revisiting Indexes for Assessing Interpretability of Fuzzy Systems

Interpretability is one of the most valuable properties of fuzzy systems. Despite the effort made by the research community for characterizing interpretability, there is not a consensus about how to measure interpretability yet. It is admitted that the analysis of interpretability is subjective because it depends on the background of the person who makes the assessment. Accordingly, an index flexible enough to fit with preferences and expectations would be appreciated from the designer but also from the user viewpoints. Hence, subjective indexes become essential for customization purposes. However, they are not enough for measuring interpretability in the broad sense. There is also a need of objective indexes to make feasible fair comparisons among different fuzzy systems designed for solving a given problem. Thus, it is necessary to look for two kinds of complementary indexes, subjective and objective ones. Moreover, they should tackle with interpretability from readability and comprehensibility viewpoints. They also must consider both structural and semantic interpretability properties. In this chapter, we give an overview on existing indexes for assessing all aspects related to interpretability of fuzzy systems. In addition, we present a conceptual framework for assessing interpretability with a customizable index which combines subjective and objective ones.