A New Monotonicity Index for Fuzzy Rule-based Systems

Lie, Meng Pang and Kai, Meng Tay and Chee, Peng Lim (2014) A New Monotonicity Index for Fuzzy Rule-based Systems. 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

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Abstract

A search in the literature reveals that mathematical conditions (usually sufficient conditions) for the Fuzzy Inference System (FIS) models to satisfy the monotonicity property have been developed. A monotonicallyordered fuzzy rule base is important to maintain the monotonicity property of an FIS. However, it may difficult to obtain a monotonically-ordered fuzzy rule base in practice. We have previously introduced the idea of fuzzy rule relabeling to tackle this problem. In this paper, we further propose a monotonicity index for the FIS system, which serves as a metric to indicate the degree of a fuzzy rule base fulfilling the monotonicity property. The index is useful to provide an indication whether a fuzzy rule base should (or should not) be used in practice, even with fuzzy rule relabeling. To illustrate the idea, the zero-order Sugeno FIS model is exemplified. We add noise as errors into the fuzzy rule base to formulate a set of non-monotone fuzzy rules. As such, the metric also acts as a measure of noise in the fuzzy rule base. The results show that the proposed metric is useful to indicate the degree of a fuzzy rule base fulfilling the monotonicity property.

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