Designing Monotone Takagi-Sugeno-Kang Fuzzy Inference Systems with New Joint Sufficient Conditions

Kerk, Yi Wen and Jong, Chian Haur and Chang, Wui Lee and Tan, Choo Jun and Tay, Kai Meng and Lim, Chee Peng (2024) Designing Monotone Takagi-Sugeno-Kang Fuzzy Inference Systems with New Joint Sufficient Conditions. Fuzzy Sets and Systems. p. 109217. ISSN 1872-6801 (In Press)

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Abstract

The Takagi-Sugeno-Kang Fuzzy Inference System (TSK-FIS) has been a well-known and useful methodology for undertaking various real-world problems. In this paper, we focus on the design of a monotone TSK-FIS model with a “grid partition” strategy for computing its firing strengths using the product T-norms. Two research questions are tackled, namely (i) what are the necessary condition and the sufficient condition for a TSK-FIS model to be monotone? (ii) how do we design a monotone TSK-FIS model with general membership functions (MFs) and consequents, such as non-convex, sub-normal, or with jump discontinuity? We first formulate a new joint necessary condition, whereby each constituent itself is a necessary condition, for designing a monotone TSK-FIS model. We then formulate a new joint sufficient condition that encompasses the joint necessary condition. Our proposed formulations allow designing TSK-FIS models with varying MFs, either convex or non-convex, normal or sub-normal, or with jump discontinuity. We also allow the fuzzy If-Then rules to have non-monotone functional consequents. Based on the new joint sufficient conditions, a set of practical guidelines is outlined for devising different monotone TSK-FIS models (i.e., zero-order TSK-FIS models as well as TSK-FIS models with functional consequents) that incorporate overlapped MFs. We also explain that the joint sufficient condition alone is not applicable to designing TSK-FIS models that compute their firing strengths with minimum T-norms. Applicability of the new sufficient condition to design monotone TSK-FIS models is demonstrated using benchmark soil erosion and failure mode and effect analysis (FMEA) problems.

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