A New Approach for Transformation-Based Fuzzy Rule Interpolation

Tianhua Chen,Changjing Shang,Fangyi Li,Jing Yang,Qiang Shen

doi:10.1109/tfuzz.2019.2949767

Tianhua Chen, Changjing Shang + Show 3 more

Open Access

https://doi.org/10.1109/tfuzz.2019.2949767

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Abstract

Fuzzy rule interpolation (FRI) is of particular significance for reasoning in the presence of insufficient knowledge or sparse rule bases. As one of the most popular FRI methods, transformation-based fuzzy rule interpolation (TFRI) works by constructing an intermediate fuzzy rule, followed by running scale and move transformations. The process of intermediate rule construction selects a user-defined number of rules closest to an observation that does not match any existing rule, using a distance metric. It relies upon heuristically computed weights to assess the contribution of individual selected rules. This process requires a move operation in an effort to force the intermediate rule to overlap with an unmatched observation, regardless of what rules are selected and how much contribution they may each make. It is, therefore, desirable to avoid this problem and also to improve the automation of rule interpolation without resorting to the user's intervention for fixing the number of closest rules. This article proposes such a novel approach to selecting a subset of rules from the sparse rule base with an embedded rule weighting scheme for the automatic assembling of the intermediate rule. Systematic comparative experimental results are provided on a range of benchmark datasets to demonstrate statistically significant improvement in the performance achieved by the proposed approach over that obtainable using conventional TFRI.

Highlights

B EING one of the cornerstones of soft computing, fuzzy set theory enables the tolerance of imprecision, uncertainty, and approximation in data and knowledge, which many problems in real life involve that conventional Boolean representation cannot handle
The purpose of this work is to show that when only a sparse rule base is available, the proposed approach can improve upon the popular state-of-the-art transformation-based fuzzy rule interpolation (TFRI)
The errors across the whole rule base are more affected by the interpolated rules than by the rules that do not fire the unmatched instances to sufficient degrees. These results collectively demonstrate that optimized transformation-based fuzzy rule interpolation (OTFRI) improves upon the conventional TFRI method

Summary

Introduction

B EING one of the cornerstones of soft computing, fuzzy set theory enables the tolerance of imprecision, uncertainty, and approximation in data and knowledge, which many problems in real life involve that conventional Boolean representation cannot handle. Fuzzy-rule-based systems [1]–[3] have been very successful in a wide range of real-world applications (e.g., [4]–[7]). In order for such systems to work, a dense fuzzy rule base is normally required to cover the entire input space such that any incoming new observations may Manuscript received October 19, 2018; revised June 12, 2019, August 2, 2019, and September 13, 2019; accepted October 9, 2019. There are many problems where knowledge about the domain is rather incomplete so that only a sparse rule base may be available. The representative value Rep(Ai) that denotes the overall geometric shape and location of the fuzzy set Ai in its corresponding domain is defined by the following: Rep(Ai)

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