Monotone interval fuzzy inference systems

In this paper, we introduce the notion of a monotone fuzzy partition, which is useful for constructing a monotone zero-order Takagi-Sugeno-Kang Fuzzy Inference System (ZOTSK-FIS). 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.