In this contribution we propose a method for generating OWA weighting vectors from the individual assessments on a set of alternatives in such a way that these weights minimize the disagreement among individual assessments and the outcome provided by the OWA operator. For measuring that disagreement we have aggregated distances between individual and collective assessments by using a metric and...

In the paper, the authors establish two identities to express higher order derivatives and integer powers of the generating function of the Chebyshev polynomials of the second kind in terms of integer powers and higher order derivatives of the generating function of the Chebyshev polynomials of the second kind respectively, find an explicit formula and an identity for the Chebyshev polynomials ...

This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebys...

Throughout this study, we continue the analysis of a recently found out Gibbs–Wilbraham phenomenon, being related to behavior Lagrange interpolation polynomials continuous absolute value function. Our study establishes error polynomial interpolants function |x| on [−1,1], using Chebyshev and Chebyshev–Lobatto nodal systems with an even number points. Moreover, respect odd cases, relevant change...

The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we need an efficient and accurate computational method for the solution of fractional differential equations. This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential ...

Tthis paper, is concerned with obtaining numerical solutions for a class of convection-diffusion equations (CDEs) with variable coefficients. Our approaches are based on collocation methods. These approaches implementing all four kinds of shifted Chebyshev polynomials in combination with Sinc functions to introduce an approximate solution for CDEs . This approximate solution can be expressed as...

When a function is singular at the ends of its expansion interval, its Chebyshev coefficients a, converge very poorly. We analyze three numerical strategies for coping with such singularities of the form (1 + x)~ log(1 f x), and in the process make some modest additions to the theory of Chebyshev expansions. The first two numerical methods are the convergence-improving changes of coordinate x =...