Analysis and Design of Functionally Weighted Single-Input-Rule-Modules Connected Fuzzy Inference Systems

The single-input-rule-modules (SIRMs) connected fuzzy inference method can efficiently solve the fuzzy rule explosion phenomenon, which usually occurs in the multivariable modeling and/or control applications. However, the performance of the SIRMs connected fuzzy inference system (SIRM-FIS) is limited due to its simple input-output mapping. In this paper, to further enhance the performance of SIRM-FIS, a functionally weighted SIRM-FIS (FWSIRM-FIS), which adopts multivariable functional weights to measure the important degrees of the SIRMs, is presented. Then, in order to show the fundamental differences of the SIRMs methods, properties of the traditional SIRM-FIS, the type-2 SIRM-FIS (T2SIRM-FIS), the functional SIRM-FIS (FSIRM-FIS), the SIRMs model with single-variable functional weights (SIRM-FW), and FWSIRM-FIS are explored. These properties demonstrate that the proposed FWSIRM-FIS has more general and complex input-output mapping than the existing SIRMs methods. Such properties theoretically guarantee that better performance can be achieved by FWSIRM-FIS. Furthermore, based on the least-squares method, a novel data-driven optimization method is presented for the parameter learning of FWSIRM-FIS. It can also be used to optimize the parameters of SIRM-FIS, T2SIRM-FIS, FSIRM-FIS, and SIRM-FW. Due to the properties of the least-squares method, the proposed parameter learning algorithm can overcome the drawbacks of the gradients-based parameter learning methods and obtain both smallest training errors and smallest parameters. Finally, to show the effectiveness and superiority of FWSIRM-FIS and the proposed optimization method, six examples and detailed comparisons are given. Simulation results show that FWSIRM-FIS can obtain better performance than the other SIRMs methods, and, compared with some well-known methods, FWSIRM-FIS can achieve similar or better performance but has much less parameters and faster training speed.