Abstract
AbstractFuzzy logic-based systems are nowadays commonly used in nonlinear function approximation when incoming data are available. Their main advantage is that the resulting rules can be interpreted understandably. Nevertheless, when the data are noisy an overfitting may occur which leads to poor accuracy and generalization ability. Prior information about the nonlinear function may improve fuzzy system performance. In this paper the case when the function is monotonic with respect to some or all variables is considered. Sufficient conditions for the monotonicity of first-order Takagi–Sugeno fuzzy systems with raised cosine membership functions are derived. Performance of the proposed fuzzy system is tested on two benchmark datasets
Funder
Czech Technical University in Prague
Publisher
Springer Science and Business Media LLC
Reference53 articles.
1. Lindskog, P., Ljung, L.: Ensuring monotonic gain characteristics in estimated models by fuzzy model structures. Automatica 36(2), 311–317 (2000)
2. Van Broekhoven, E., De Baets, B.: Only smooth rule bases can generate monotone Mamdani–Assilian models under center-of-gravity defuzzification. IEEE Trans. Fuzzy Syst. 17(7), 1157–1174 (2009)
3. Hušek, P.: On monotonicity of Takagi–Sugeno fuzzy systems with ellipsoidal regions. IEEE Trans. Fuzzy Syst. 24, 1673–1678 (2016)
4. Doumpos, M., Pasiouras, F.: Developing and testing models for replicating credit ratings: a multicriteria approach. Comput. Econ. 25(4), 327–341 (2005)
5. Li, C., Yi, J., Zhao, D.: Analysis and design of monotonic type-2 fuzzy inference systems. IEEE Int. Conf. Fuzzy Syst. 2009, 1193–1198 (2009)