Designing Monotone Takagi-Sugeno-Kang Fuzzy Inference Systems with New Joint Sufficient Conditions - Kerk, Yi Wen; Jong, Chian Haur; Chang, Wui Lee; Tan, Choo Jun; Tay, Kai Meng; Lim, Chee Peng (Elsevier Inc., 2024)
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.