Modeling high interest areas in descriptive TS fuzzy rule based systems

A descriptive Takagi-Sugeno fuzzy rule based system suffers under the curse of dimensionality since the number of rules is equal to a fuzzy system with a fully filled up decision table. By defining high interest areas as areas where the input space is covered with many membership functions to achieve an acceptable error, the consequence is an often inappropriate fine grid of membership functions in orthogonal arranged low interest areas and an exponential increased number of rules. A possible solution is that the fine grid of membership functions, originated by the projection of a high interest area on the concerning single input variables, is only used if all elements of the input vector are situated in a high interest area. To guarantee the interpretability of a descriptive fuzzy rule based system the additional membership functions caused by high interest areas should fit in the coarser grid by retaining the interpretability of all linguistic variables. This paper propose an approach using evolutionary computation to identify high interest areas and using bsplines as membership functions to maintain a maximum of system interpretability.