Second interpolation in fuzzy control
Boris Kovalerchuk · Proceedings of IEEE 5th International Fuzzy Systems · 2002
New approaches are required to develop effective fuzzy controllers. We present an "interpolation" approach, which solves some difficulties of the current approach. Our controller gives practically the same precision as a Mamdani controller for a wide range of one- and two-dimensional state spaces. This interpolation approach eliminates the following heuristic elements of a Mamdani controller: (ii) defuzzification with the center of gravity, (ii) tuning of antecedent and consequent membership functions by "blind" optimization and (iii) min and max operations for logical connectives. We show that the alternative interpolation is a universal approximator like a Mamdani controller itself. The deviation between Mamdani and our interpolation is /spl les/5.05% of the fuzzy set's support for a two-dimensional case and /spl les/2.07% for a one dimensional case. The alternative interpolation is much simpler than a Mamdani controller. It decreases runtime and simplifies controller hardware design.