A New Monotonicity Index for Fuzzy Rule-based Systems

• Main Authors: Lie, Meng Pang, Kai, Meng Tay, Chee, Peng Lim
• Format: E-Article
• Language: English
• Published: IEEE 2014
• Subjects: TA Engineering (General). Civil engineering (General)
• Online Access: http://ir.unimas.my/id/eprint/5182/1/a%20new%20monotonicity%20index%20for%20fuzzy%20rule-based%20systems%20%28abstract%29.pdf; http://ir.unimas.my/id/eprint/5182/
• Institution: Universiti Malaysia Sarawak

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.