A practical algorithm for representing polynomials of two variables by fuzzy systems with accuracy O\((h^4)\) (Q5931182)

The fuzzy system is based on the cubic interpolation of polynomials of the form\break \(\displaystyle\sum_{i,j}c_{ij}B_i(x)B_j(y)\) where \(B_i(x)\) and \(B_j(y)\) are cubic \(B\)-splines. In this paper an algorithm is presented for representing polynomials in two variables by a fuzzy system.NEWLINENEWLINENEWLINEIt is proved that this fuzzy system is an exact representation of the cubic spline interpolation function and hence the evaluation error for the fuzzy system is of order \(O(h^4)\). An algorithm to compute the spline coefficients explicitly without solving the matrix equation involved is also included along with evaluation results of the fuzzy-system for various examples.