A hybrid continuity preserving inference strategy to speed up Takagi-Sugeno multiobjective genetic fuzzy systems

The most popular inference method in Takagi-Sugeno (TS) fuzzy systems is the weighted averaging (WA), whereas the most investigated inference method in fuzzy rule-based classifier is probably the winner-takes-all (WTA). This paper first shows the time complexities associated with WA and WTA inference methods in Takagi-Sugeno fuzzy rule-based systems, also highlighting the strengths and the weaknesses of both approaches. Then it argues that using a hybrid of the two inference methods, namely the WTA during identification and the WA during the evaluation, allows advantaging of the strong points of the two methods, without inheriting most of their weakness. In particular, the hybrid formulation has a nice property which can be even mandatory in particular applications: it both guarantees that the TS system is continuous (provided that infinite support membership functions are used) and that it performs an approximate reasoning, by combining the conclusions of more than one rule. The interesting features of the hybrid method are demonstrated on a multiobjective genetic rule learning framework used for regression.