This paper presets a method including a combination of the wavelet transform and fuzzy function approximation (FFA) for high impedance fault (HIF) detection in distribution electricity network. Discrete wavelet transform (DWT) has been used in this paper as a tool for signal analysis. With studying different types of mother signals, detail types and feeder signal, the best case is selected. The...

Tree approximation is a form of nonlinear wavelet approximation that appears naturally in applications such as image compression and entropy encoding. The distinction between tree approximation and the more familiar n-term wavelet approximation is that the wavelets appearing in the approximant are required to align themselves in a certain connected tree sturcture. This makes their positions eas...

We present a method for hierarchical data approximation using quadratic simplicial elements for domain decomposition and field approximation. Higher-order simplicial elements can approximate data better than linear elements. Thus, fewer quadratic elements are required to achieve similar approximation quality. We use quadratic basis functions and compute best quadratic simplicial spline approxim...

Fuzzy systems comprise one of the models best suited to function approximation problems, but due to the non linear dependencies between the parameters that define the system rules, the solution search space for this type of problems contains many local optima. Another important issue is the identification of the optimum structure for the fuzzy system. Depending on the complexity of the model, d...

The term approximate reasoning (AR) refers to methods and methodologies that enable reasoning with imprecise inputs to obtain meaningful outputs. AR schemes involving fuzzy sets are one of the best known applications of fuzzy logic in the wider sense. Fuzzy Inference Systems (FIS) have many degrees of freedom, viz., the underlying fuzzy partition of the input and output spaces, the fuzzy logic ...

In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

The existence of common fixed points is established for the mappings where T is asymptotically f -pseudo-contraction on a nonempty subset of a Banach space. As applications, the invariant best simultaneous approximation and strong convergence results are proved. Presented results are generalizations of very recent fixed point and approximation theorems of Khan and Akbar 2009 , Chen and Li 2007 ...

we present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with lr fuzzy variables. as solutions, notions of exact and approximate solutions are considered. we transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. if the corresponding crisp system is incompatible, then the fuzzy ...

Rough set theory has attracted much attention in modeling with imprecise and incomplete information. A generalized approximation space, called fuzzy probability approximation space has been proposed by introducing probability into fuzzy approximation space. The novel definition combines three types of uncertainty into a model. Information or knowledge is considered as a partition of the univers...