A fuzzy rule interpolation technique based on bi-splines in multiple input systems

This work deals with the problem of nonlinear interpolative reasoning in a sparse fuzzy rule base with multiple input. First of all, the authors introduce a method of fuzzy rule interpolation based on bi-splines and the notion of a fuzzy interpolation function (we call it a fuzzy spline surface in the case of two-input). Then, we propose a method to construct fuzzy partitions (a new dense rule base) through such a fuzzy function, which enables us to execute any conventional approximate reasoning method for arbitrary input.