جستجوی مقالات مرتبط با کلیدواژه « fuzzy linear system » در نشریات گروه « ریاضی »

Systems of simulations linear equations play major role in various areas such as mathematics, statistics, and social sciences. Since in many applications, at least some of the system’s parameters and measurements are represented by fuzzy rather than crisp numbers, therefore, it is important to develop mathematical models and numerical procedures that would appropriately treat general fuzzy linear systems and solve them. In this paper, a new method based on fuzzy operations approach for solving Fuzzy Linear System (FLS) is introduced. The related theorems are proved in details. Finally, the proposed method is illustrated by solving two numerical examples.

In this manuscript, we introduce a new class of fuzzy problems, namely ``fuzzy inclusion linear systems" and propose a fuzzy solution set for it. Then, we present a theoretical discussion about the relationship between the fuzzy solution set of a fuzzy inclusion linear system and the algebraic solution of a fuzzy linear system. New necessary and sufficient conditions are derived for obtaining the unique algebraic solution for a fuzzy linear system. Also, all new concepts are illustrated by numerical examples.

In this paper, we use parametric form of fuzzy number and we converta fuzzy linear system to two linear system in crisp case. Conditions for the existence of a minimal solution to $mtimes n$ fuzzy linear equation systems are derived and a numerical procedure for calculating the minimal solution is designed. Numerical examples are presented to illustrate the proposed method.

A s we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system''s parameters are proposed as fuzzy numbers is very important in fuzzy set theory. For this reason, many researchers have used various numerical methods to solve fuzzy linear systems. In this paper, we define the concepts of midpoint and radius functions for a fuzzy number, midpoint and radius vectors for a fuzzy number vector and midpoint and radius systems for a fuzzy linear system. All these new definitions are defined based on the parametric form of fuzzy numbers. Then, by these new concepts, we propose a simple method to solve a fuzzy linear system and obtain it''s algebraic solution. Also, we present a sufficient condition for the obtained solution vector to be always a fuzzy vector. Finally, several numerical examples are given to show the efficiency and capability of the proposed method.

In this paper, we apply the homotopy analysis method (HAM) for solving fuzzy linear systems and present the necessary and sufficient conditions for the convergence of series solution obtained via the HAM. Also, we present a new criterion for choosing a proper value of convergence-control parameter $hbar$ when the HAM is applied to linear system of equations. Comparisons are made between the results of the HAM and several well-known numerical algorithms such as Jacobi method (JM), Gauss-Seidel method (GSM), successive over relaxation method (SOR), Adomian decomposition method (ADM) and homotopy perturbation method (HPM).

In this paper, we investigate the general fuzzy linear system of equations. The main aim of this paper is based on the embedding approach. We find the necessary and sufficient conditions for the existence of fuzzy solution of the mentioned systems. Finally, Numerical examples are presented to more illustration of the proposed model.

In this paper, we propose the least-squares method for computing the positive solution of a $mtimes n$ fully fuzzy linear system (FFLS) of equations, where $m > n$, based on Kaffman's arithmetic operations on fuzzy numbers that introduced in [18]. First, we consider all elements of coefficient matrix are non-negative or non-positive. Also, we obtain 1-cut of the fuzzy number vector solution of the non-square FFLS of equations by using pseudoinverse. If 1-cuts vector is non-negative, we solve constrained least squares problem for computing left and right spreads. Then, in the special case, we consider 0 is belong to the support of some elements of coefficient matrix and solve three overdetermined linear systems and if the solutions of these systems held in non-negative fuzzy solutions then we compute the solution of the non-square FFLS of equations. Else, we solve constrained least squares problem for obtaining an approximated non-negative fuzzy solution. Finally, we illustrate the efficiency of the proposed method by solving some numerical examples.

According to fuzzy arithmetic, general dual fuzzy linearsystem (GDFLS) cannot be replaced by a fuzzy linear system (FLS). Inthis paper, we use new notation of fuzzy numbers and convert a GDFLSto two linear systems in crisp case, then we discuss complexity of theproposed method. Conditions for the existence of a unique fuzzy solutionto n × n GDFLS are derived.

In this paper, a numerical method for nding minimal solution of a mn fully fuzzy linear system of the form ~ A~x = ~b based on pseudo inverse calculation, is given when the central matrix of coecients is row full rank or column full rank, and where A~ is a non-negative fuzzy mn matrix, the unknown vector ~x is a vector consisting of n non-negative fuzzy numbers and the constant ~b is a vector consisting of m non-negative fuzzy numbers.

In this paper, normal equations for singular fuzzy linear systems is proposed. The principal application of the normal equations is to systems of equations that are inconsistent. The results are explained by solving some numerical examples.