Fuzzy System Of Linear Equations Research Articles

Solving System of Fuzzy Linear Equations

Solving System of Fuzzy Linear Equations

Block Jacobi two-stage method with Gauss–Sidel inner iterations for fuzzy system of linear equations

In this paper we study Block two-stage iterative method for finding the approximate solution of fuzzy system of linear equation (FSLE) with convergence conditions. The application of this method is solving large linear system on parallel computer. Algorithm is illustrated by solving some numerical examples.

Fuzzy linear systems of the form [formula omitted

Linear systems of equations, with uncertainty on the parameters, play a major role in several applications in various areas such as economics, finance, engineering and physics. This paper investigates fuzzy linear systems of the form A 1 x + b 1 = A 2 x + b 2 with A 1 , A 2 square matrices of fuzzy coefficients and b 1 , b 2 fuzzy number vectors. The aim of this paper is twofold. First, we clarify the link between interval linear systems and fuzzy linear systems. Second, a generalization of the vector solution of Buckley and Qu [Solving systems of linear fuzzy equations, Fuzzy Sets and Systems 43 (1991) 33–43] to the fuzzy system A 1 x + b 1 = A 2 x + b 2 is provided. In particular, we give the conditions under which the system has a vector solution and we show that the linear systems Ax = b and A 1 x + b 1 = A 2 x + b 2 , with A = A 1 - A 2 and b = b 2 - b 1 , have the same vector solutions. Moreover, in order to find the vector solution, a simple algorithm is proposed.

Steepest descent method for system of fuzzy linear equations

In this paper the steepest descent method, for solving system of fuzzy linear equation is considered. The method in detail is discussed and followed by convergence theorem and illustrated by solving some numerical examples.

A SOLUTION FOR SYSTEMS OF LINEAR FUZZY EQUATIONS IN SPITE OF THE NON-EXISTENCE OF A FIELD OF FUZZY NUMBERS

In this paper we investigate whether the fuzzy arithmetic based on Zadeh's extension principle could be improved by redefining the fuzzy addition and multiplication so that the class of fuzzy numbers combined with these operations would constitute a field. We will prove that such a fuzzy arithmetic does not exist. This has important consequences for solving systems of linear fuzzy equations. Despite the lack of inverses, we propose a method to solve approximately such systems.

LU decomposition method for solving fuzzy system of linear equations

In this paper LU decomposition method, for solving fuzzy system of linear equations is considered. We consider the method in spatial case when the coefficient matrix is symmetric positive definite. The method in detail is discussed and followed by convergence theorem and illustrated by solving some numerical examples.

The Adomian decomposition method for fuzzy system of linear equations

In this paper the application of the Adomian method for solving Fuzzy system of linear equations ( FSLE) is considered. For a FSLE has been shown that the Adomian decomposition method is equivalent to the Jacobi iterative method [Appl. Math. Comput., in press]. The algorithm is illustrated by solving some numerical examples.

Successive over relaxation iterative method for fuzzy system of linear equations

In this paper the Gauss–Sidel iterative method in Allahviranloo [Appl. Math. Comput., in press], for solving Fuzzy system of linear equations (FSLE) is transformed to the successive over relaxation (SOR) method. This method is discussed in detail and followed by convergence theorem. Algorithm is compared with the Gauss–Sidel method by solving a numerical example.

Numerical methods for fuzzy system of linear equations

In this paper numerical algorithms for solving `fuzzy system of linear equations' (FSLE) are considered. Schemes based on the iterative Jacobi and Gauss Sidel methods in detail are discussed and there are followed by convergence theorems. Algorithms are illustrated by solving some numerical examples.

Solving fuzzy equations using evolutionary algorithms and neural nets

In this paper we use evolutionary algorithms and neural nets to solve fuzzy equations. In Part I we: (1) first introduce our three solution methods for solving the fuzzy linear equation A¯X¯ + B¯= C¯; for X¯ and (2) then survey the results for the fuzzy quadratic equations, fuzzy differential equations, fuzzy difference equations, fuzzy partial differential equations, systems of fuzzy linear equations, and fuzzy integral equations; and (3) apply an evolutionary algorithm to construct one of the solution types for the fuzzy eigenvalue problem. In Part II we: (1) first discuss how to design and train a neural net to solve A¯X¯ + B¯= C¯ for X¯ and (2) then survey the results for systems of fuzzy linear equations and the fuzzy quadratic.

Iteration algorithms for solving a system of fuzzy linear equations

In this paper, we discuss the solution of a system of fuzzy linear equations, X=AX+U, and its iteration algorithms where A is a real n×n matrix, the unknown vector X and the constant U are all vectors consisting of n fuzzy numbers, and the addition, scale-multiplication are defined by Zadeh's extension principle. After introducing a metric between two fuzzy vectors, we prove that the system has unique solution if ∥A∥ ∞<1 . We also give the convergence and the error estimation for using simple iteration to obtain the solution. Finally, we give the convergence and the error estimation of successive iteration sequence for obtaining the solution.

Fuzzy linear systems

Abstract Fuzzy linear systems of equations and inequalities over a bounded chain are studied both from theoretical and computational points of view. A unified approach is presented for solving such systems, completed with polynomial time algorithms. The main results are concerned with establishing the consistency of the system, computing all kinds of solutions, or marking the contradictory equations (respectively inequalities) if the system is inconsistent. Applications in fuzzy linear programming, multivalued logic, fuzzy matrix equations or inequalities, fuzzy relation equations or inclusions, fuzzy automata and medicine are presented.

Solving systems of linear fuzzy equations

In this paper we wish to construct solutions for x to the fuzzy matrix equation Ax = b when the elements in A and b are triangular fuzzy numbers. A is square and always non-singular. We argue that the previous method of solving for x , based on the extension principle and regular fuzzy arithmetic, should be abandoned since it too often fails to produce a solution. We present six new solutions of which we show that five are identical. We then adopt the common value X of these five new solutions as our solution to Ax = b . We show that X is a fuzzy vector which is the generalization to R n of real fuzzy numbers. We also show how these results pertain to, and extend, previous research on this problem within the area of interval analysis.