Fuzzy Integrals and Smoothing Filters

Symmetrizing Smoothing Filters

We study a general class of nonlinear and shift-varying smoothing filters that operate based on averaging. This important class of filters includes many well-known examples such as the bilateral filter, nonlocal means, general adaptive moving average filters, and more. (Many linear filters such as linear minimum mean-squared error smoothing filters, Savitzky–Golay filters, smoothing splines, an...

Demystifying Symmetric Smoothing Filters

Many patch-based image denoising algorithms can be formulated as applying a smoothing filter to the noisy image. Expressed as matrices, the smoothing filters must be row normalized so that each row sums to unity. Surprisingly, if we apply a column normalization before the row normalization, the performance of the smoothing filter can often be significantly improved. Prior works showed that such...

Fuzzy Number Fuzzy Measures and Fuzzy Integrals

By using the concepts of fuzzy number fuzzy measures and fuzzy valued functions a theory of fuzzy integrals is investigated. In this paper we have established the fuzzy version of Generalised monotone Convergence theorem and generalised Fatous lemma. 1. Introduction In the preceding paper [2], it is introduced that a concept of fuzzy number fuzzy measures, defined the fuzzy integral of a functi...

Quadrature Rules for Fuzzy Integrals

General Minkowski type and related inequalities for seminormed fuzzy integrals

Minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. Also related inequalities to Minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. Several examples are given to illustrate the validity of theorems. Some results on Chebyshev and Minkowski type inequalities are obtained.