Using classic approximation techniques for approximate reasoning

An approach to fuzzy reasoning is proposed, that is built on classic approximation techniques. More precisely, fuzzy relations are approximated by B-spline surfaces. The main advantages are: a well founded approximation theory, great approximation capabilities, and the possibility to interpret the B-spline basis as fuzzy rules. In addition, natural representations of positive rules (support distributions, Mamdani-inference) and negative rules (possibility distributions, Godel-inference) are presented. In this context, a very fast inference mechanism for multi-stage reasoning is proposed. In the best case, the computation costs are the square number of rules. Altogether the new method provides a memory saving representation of fuzzy rule bases, a fast inference mechanism and high approximation power. These features recommend the method not only for control purposes but also in more general settings of approximate reasoning