A Fast Inference and Type-Reduction Process for Constrained Interval Type-2 Fuzzy Systems

Pasquale Dralterio,Jonathan M Garibaldi,Robert I John,Christian Wagner

doi:10.1109/tfuzz.2020.3018379

Pasquale Dralterio, Jonathan M Garibaldi + Show 2 more

Open Access

https://doi.org/10.1109/tfuzz.2020.3018379

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Abstract

Constrained interval type-2 (CIT2) fuzzy sets have been introduced to preserve interpretability when moving from type-1 to interval type-2 (IT2) membership functions. Although they can be used to produce type-2 fuzzy systems with enhanced explainability, so far, the latter comes at the expense of high computational cost. Specifically, the exhaustive type-reduction method for CIT2 Mamdani systems has been shown to be too slow to be used in practical applications and even the current approximation procedure is much slower than modern type-reduction algorithms used for IT2 fuzzy sets. In this article, a novel type-reduction procedure for CIT2 sets is presented, based on the concept of switch indices. The algorithm is applied on a real-world classification problem and compared to other type-reduction approaches used in IT2 and CIT2 systems. In the case studies presented, the new algorithm is significantly faster than the exhaustive and sampling CIT2 approaches while keeping the high level of interpretability of the type-reduction operation that characterizes CIT2 fuzzy sets.

Highlights

In recent years, there has been a growing trend for more explainable and transparent AI systems that has led to the creation of the new research field of explainable artificial intelligence (XAI) [1], [2]
While the interpretability of type-1 (T1) FLS has already been examined in some research (e.g. [3]), the same cannot be said for interval type-2 (IT2) [7] and general type2 (GT2) [8] fuzzy logic systems
The data shows that the IT2 and the 2 constrained interval type-2 (CIT2) FLSs perform better than the T1 one; both the CIT2 show a higher accuracy than the IT2 FLS, with the CIT2 FLS with the sampling method having the best performance (0.277% better than the switch index algorithm)

Summary

Introduction

There has been a growing trend for more explainable and transparent AI systems that has led to the creation of the new research field of explainable artificial intelligence (XAI) [1], [2]. The rule-based structure together with the use of linguistic labels [4], allow for the creation of fuzzy logic systems (FLS) that give reliable predictions in AI tasks and have a high level of understandability for both an expert and nonexpert audience For this reason, FL represents a valuable tool in XAI which has already been successfully applied in some real-world problems [5], [6]. Keeping the semantic meaning between a GT2 or IT2 fuzzy set and the linguistic label it represents may be challenging, as the footprint of uncertainty (FOU, [10]) contains embedded sets (ES) that in some contexts may represent implausible relations between the data [11], [12] These issues have led to the creation of a restricted version of type-2 fuzzy sets called constrained type (CT2) fuzzy sets [13] and constrained interval type-2 (CIT2) [14], [15] fuzzy sets. CIT2 FS impose restrictions on the shape of the FOU and the embedded sets that lead to more interpretable FLS compared to their IT2 counterparts [14]

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