Abstract We point out that B spline basis functions are naturally de ned membership functions for fuzzy logic systems i e the speci cation of these functions depends only on the partition points of each linguistic variables no more necessarily also on the additional parameters if normal set functions are used Based on B spline basis functions a fuzzy controller can be constructed which works li...

In this paper, Semi-orthogonal (SO) B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of linear and non-linear second order Fredholm integro-differential equations. The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this functions are presented to reduce the solution of linear and...

By a d-dimensional B-spline object (denoted as ), we mean a B-spline curve (d = 1), a B-spline surface (d = 2) or a B-spline volume (d = 3). By regularization of a B-spline object we mean the process of relocating the control points of such that they approximate an isometric map of its definition domain in certain directions and is shape preserving. In this paper we develop an efficient regul...

In this paper we introduce a numerical approach that solves optimal control problems (OCPs) using collocation methods. This approach is based upon B-spline functions. The derivative matrices between any two families of B-spline functions are utilized to reduce the solution of OCPs to the solution of nonlinear optimization problems. Numerical experiments confirm our theoretical findings.

In this paper, we introduce the notion of a normalized radial basis function. In the univariate case, taking these basis functions in combinations determined by certain discrete differences leads to the B-spline basis. In the bivariate case, these combinations lead to a generalization of the B-spline basis to the surface case. Subdivision rules for the resulting basis functions can easily be de...

It is proved that, among all nonnegative bases of its space, the B-spline basis is optimally stable for evaluating spline functions.

O. Ismail, Senior Member, IEEE Abstract— This paper presents an efficient method for degree elevation of interval B-spline curves. The four fixed Kharitonov's polynomials (four fixed B-spline curves) associated with the original interval B-spline curve are obtained. The method is based on the matrix identity. The B-spline basis functions are represented as linear combinations of the B-splines o...

Image encryption is one of most useful way of securing image data. Traditional data security algorithms are also used over images but due to the bulkiness of image data they are not useful. Chaotic sequences play a very good role in image cryptographic system, due to their high sensitivity to initial condition and other properties. In this paper, B-spline functions of first three orders are stu...

It is proved that, among all nonnegative bases of its space, the B-spline basis is optimally stable for evaluating spline functions.