Monotone Interval Fuzzy Inference Systems

• Main Authors: Yi, Wen Kerk, Tay, Kai Mei, Lim, Chee Peng
• Format: Article
• Language: English
• Published: IEEE Xplore 2019
• Subjects: Q Science (General); QA Mathematics
• Online Access: http://ir.unimas.my/id/eprint/27822/1/Fuzzy.pdf; http://ir.unimas.my/id/eprint/27822/; https://ieeexplore.ieee.org/document/8632681

—In this paper, we introduce the notion of a monotone fuzzy partition, which is useful for constructing a monotone zeroorder Takagi–Sugeno–Kang Fuzzy Inference System (ZOTSKFIS). It is known that a monotone ZOTSK-FIS model can always be produced when a consistent, complete, and monotone fuzzy rule base is used. However, such an ideal situation is not always available in practice, because a fuzzy rule base is susceptible to uncertainties, e.g., inconsistency, incompleteness, and nonmonotonicity. As a result, we devise an interval method to model these uncertainties by considering the minimum interval of acceptability of a fuzzy rule, resulting in a set of monotone interval-valued fuzzy rules. This further leads to the formulation of a Monotone Interval Fuzzy Inference System (MIFIS) with a minimized uncertainty measure. The proposed MIFIS model is analyzed mathematically and evaluated empirically for the Failure Mode and Effect Analysis (FMEA) application. The results indicate that MIFIS outperforms ZOTSK-FIS, and allows effective decision making using uncertain fuzzy rules solicited from human experts in tackling real-world FMEA problems.