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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 832831, 10 pages
http://dx.doi.org/10.1155/2013/832831
Research Article

Some Fuzzy-Wavelet-Like Operators and Their Convergence

Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

Received 25 January 2013; Accepted 20 May 2013

Academic Editor: Tofigh Allahviranloo

Copyright © 2013 R. Ezzati et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Firstly, we define some new fuzzy-wavelet-like operators via a real-valued scaling function to approximate the continuous fuzzy functions of one and two variables. Then, by using the modulus of continuity, we prove their pointwise and uniform convergence with rates to the fuzzy unit operator . Using these fuzzy-wavelet-like operators, we present some numerical examples to illustrate the applicability of the proposed method. Also, we give a new method to approximate the integration of continuous fuzzy real-number-valued function of two variables by using the fuzzy-wavelet-like operator.