General MISO Takagi-Sugeno fuzzy systems with simplified linear rule consequent as universal approximators for control and modeling applications

We investigate analytical structure of a general class of MISO Takagi-Sugeno (TS) fuzzy systems (1985) that use arbitrary TS fuzzy rules with our recently introduced simplified linear rule consequent. Other system components in this study are general: arbitrary continuous input fuzzy sets, any type of fuzzy logic AND and the generalized defuzzifier containing the widely used centroid defuzzifier as a special case. We have proved that the general MISO TS fuzzy systems are: (1) nonlinear variable gain controllers when implemented as controllers, (2) nonlinear time-varying auto-regressive with the extra input (ARX) models when implemented as models, and (3) nonlinear infinite impulse response or finite impulse response filters when implemented as filters. Further, we have constructively proved that the general TS fuzzy systems with the simplified linear rule consequent are universal approximators. The practical implication is that these fuzzy systems, with much fewer design parameters in the rules, are always able to produce solutions to control, modeling and filtering problems