Monotone Interval Fuzzy Inference Systems

Yi, Wen Kerk and Tay, Kai Mei and Lim, Chee Peng (2019) Monotone Interval Fuzzy Inference Systems. IEEE Transactions on Fuzzy Systems, 27 (11). pp. 2255-2264. ISSN 1063-6706

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Abstract

—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.

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