FUZZY WAVELET TYPE OPERATORS

Abstract

The basic wavelet type operators A_k, B_k, C_k, D_k, k in Z were studied extensively in the real case (see [2]). Here they are extended to the fuzzy setting and are defined similarly via a real valued scaling function. Their pointwise and uniform convergence with rates to the fuzzy unit operator I is established. The produced Jackson type inequalities involve the fuzzy first modulus of continuity and usually are proved to be sharp, in fact attained. Furthermore all fuzzy wavelet type operators A_k, B_k, C_k, D_k preserve monotonicity in the fuzzy sense. Here we do not assume any kind of orthogonality condition on the scaling function varphi, and the operators act on fuzzy valued continuous functions over R.