Interpolation in structured fuzzy rule bases

Fuzzy-rule-based systems are important in many control engineering applications. In real problems, often the number of input variables is very high, but a few or maximally a few dozen variables dominate the system in a certain area of the state space. The subset of variables changes when the working point changes. Hierarchically structured rule bases are introduced in which sub-rule-bases contain only subsets of the input variables. A fuzzy partition of the state space is applied for structuring of the total input universe of discourse. While application of the corresponding sub-rule-base in the middle of a fuzzy subset of X is unambiguous, the twilight zones, i.e., areas belonging to different subsets to a greater than 0 degree, form a serious theoretical problem. The idea of interpolation based on cylindric extensions of the subspaces is introduced, and the necessary formulas are presented. Some examples are shown