Deakin University

File(s) under permanent embargo

On the monotonicity property of the TSK fuzzy inference system: the necessity of the sufficient conditions and the monotonicity test

journal contribution
posted on 2018-08-01, 00:00 authored by C Y Teh, K M Tay, Chee Peng LimChee Peng Lim
The sufficient conditions for satisfying the monotonicity property of the Takagi–Sugeno–Kang (TSK) fuzzy inference system (FIS) have shown to be useful in many different applications. However, the related sufficient and necessary conditions are still unknown. As such, even when the sufficient conditions are violated, the TSK FIS model may still able to satisfy the monotonicity property. Therefore, the monotonicity test is used as an approximated method to determine the validness of the monotonicity property. To the best of our knowledge, the use of the monotonicity test in FIS is new. In this paper, we focus on single-input zero-order TSK FIS with Gaussian fuzzy membership functions. An algorithm to test the monotonicity property, either accepting or rejecting an TSK FIS model of being monotone, is devised and analyzed. The relationship between TSK FIS and its capability of satisfying the monotonicity property, along with the sufficient conditions and the outcome of the monotonicity test, is established through a Monte Carlo simulation. The Monte Carlo simulation is a useful necessity test for the sufficient conditions. We define a necessity measure of the sufficient conditions (NMSC) as the probability that a randomly generated monotone TSK FIS model (evaluated based on the monotonicity test algorithm) satisfies the sufficient conditions. We empirically show that the NMSC score reduces with increasing number of fuzzy rules. In addition, an application of the TSK FIS model to failure modes and effects analysis is demonstrated. As compared with the sufficient conditions, a better FIS-based model with a lower error measure can be obtained using the monotonicity test. The outcome indicates the effectiveness of the monotonicity test for designing low-dimensional TSK FIS models with large numbers of fuzzy rules.



International journal of fuzzy systems






1915 - 1924




Cham, Switzerland







Publication classification

C1 Refereed article in a scholarly journal

Copyright notice

2018, Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany, part of Springer Nature