On Ordered Weighted Averaging Operator and Monotone Takagi–Sugeno–Kang Fuzzy Inference Systems
研究了Takagi-Sugeno-Kang模糊推理系统单调性的必要和充分条件，基于有序加权平均算子推导了充分条件，并通过故障模式与影响分析和图像处理案例验证了方法的有效性。
The necessary and/or sufficient conditions for a Takagi-Sugeno-Kang Fuzzy Inference System (TSK-FIS) to be monotone has been a key research direction in the last two decades. In this article, we first define fuzzy membership functions (FMFs) with single and continuous support; and consider TSK-FIS with a grid partition strategy for computing its firing strengths with product T-norm (here after denoted as TSK-FIS-product). We also define a more general joint necessary condition, whereby each constituent itself is a necessary condition for the TSK-FIS-product model. The first necessary condition indicates that the normalized firing strength must not be indeterminate (i.e., 0/0), i.e., susceptible to the tomato classification problem. The second necessary condition indicates that all restricted consequents of fuzzy if-then rules must be defined. Based on the principle of the ordered weighted averaging (OWA) operator as well as the concept of increasing orness in OWA and hyperboxes, a general joint sufficient condition for a TSK-FIS-product model to be monotone is derived. Three case studies of the developed methods for undertaking failure mode and effect analysis (FMEA) and image processing tasks are presented. The results are compared, analyzed, and discussed, demonstrating the usefulness of our developed methods.