More on Gaussian Quadratures for Fuzzy Functions
نویسنده
چکیده
In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi, Gaussian quadratures for approximate of fuzzy integrals, Applied Mathematics and Computation 170 (2005) 874-885]. The obtained results are illustrated by solving some numerical examples. Keywords—Guassian quadrature rules, Fuzzy number, Fuzzy integral, Fuzzy solution.
منابع مشابه
TIME-VARYING FUZZY SETS BASED ON A GAUSSIAN MEMBERSHIP FUNCTIONS FOR DEVELOPING FUZZY CONTROLLER
The paper presents a novel type of fuzzy sets, called time-Varying Fuzzy Sets (VFS). These fuzzy sets are based on the Gaussian membership functions, they are depended on the error and they are characterized by the displacement of the kernels to both right and left side of the universe of discourse, the two extremes kernels of the universe are fixed for all time. In this work we focus only on t...
متن کاملOn Generalized Gaussian Quadratures\ for Exponentials and Their Applications
We introduce new families of Gaussian-type quadratures for weighted integrals of exponential functions and consider their applications to integration and interpolation of bandlimited functions. We use a generalization of a representation theorem due to Carathéodory to derive these quadratures. For each positive measure, the quadratures are parameterized by eigenvalues of the Toeplitz matrix con...
متن کاملExtended Gaussian quadratures for functions with an end-point singularity of logarithmic type
The extended Gaussian quadrature rules are shown to be an efficient tool for numerical integration of wide class of functions with singularities of logarithmic type. The quadratures are exact for the functions pol1n−1(x) + lnx pol2n−1(x) , where pol1n−1(x) and pol2n−1(x) are two arbitrary polynomials of degree n−1 and n is the order of the quadrature formula. We present an implementation of num...
متن کاملA Flexible Link Radar Control Based on Type-2 Fuzzy Systems
An adaptive neuro fuzzy inference system based on interval Gaussian type-2 fuzzy sets in the antecedent part and Gaussian type-1 fuzzy sets as coefficients of linear combination of input variables in the consequent part is presented in this paper. The capability of the proposed method (we named ANFIS2) for function approximation and dynamical system identification is remarkable. The structure o...
متن کاملA Nonlinear Optimization Procedure for Generalized Gaussian Quadratures
Gaussian quadratures for a broad class of functions. While some of the components of this algorithm have been previously published, we present a simple and robust scheme for the determination of a sparse solution to an underdetermined nonlinear optimization problem which replaces the continuation scheme of the previously published works. The performance of the resulting procedure is illustrated...
متن کامل