Interpretability Improvements to Find the Balance Interpretability-Accuracy in Fuzzy Modeling: An Overview

Abstract

Abstract. System modeling with fuzzy rule-based systems (FRBSs), i.e. fuzzy modeling (FM), usually comes with two contradictory requirements in the obtained model: the interpretability, capability to express the behavior of the real system in an understandable way, and the accuracy, capability to faithfully represent the real system. While linguistic FM (mainly developed by linguistic FRBSs) is focused on the interpretability, precise FM (mainly developed by Takagi-Sugeno-Kang FRBSs) is focused on the accuracy. Since both criteria are of vital importance in system modeling, the balance between them has started to pay attention in the fuzzy community in the last few years.The chapter analyzes mechanisms to find this balance by improving the interpretability in linguistic FM: selecting input variables, reducing the fuzzy rule set, using more descriptive expressions, or performing linguistic approximation; and in precise FM: reducing the fuzzy rule set, reducing the number of fuzzy sets, or exploiting the local description of the rules.

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“…This new definition allows that the SoH is inferred from the learnt parameters of the model without the need of a "virtual lab" relaxation experiment. There are many different contributions regarding the balance between accuracy and interpretability in FRBS [25]. Most of these studies are intended to improve the linguistic interpretability of models that are intended for verbal communication (i.e., for explaining the model properties to a human expert).…”

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“…Unfortunately, such a kind of comparison is useful in particular to compare the accuracy of models rather than their interpretability. Approaches can be proposed in order to balance accuracy and interpretability in fuzzy modelling [11].…”

Interpretability of fuzzy linguistic summaries

“…It has been extensively studied in the case of fuzzy rule-based systems [1,2,3,4], which have been the most widespread within all fuzzy modelling methods, mainly because of the early success of fuzzy expert systems and fuzzy control, both based on rules of the form "if V 1 is A 1 and V 2 is A 2 , ..., then W is B". These studies point out the difficulty to assess interpretability and provide various kinds of properties involved in its evaluation.…”