Abstract
Several authors have proposed different methods to find the solution of fully fuzzy linear systems (FFLSs) that is, fuzzy linear system with fuzzy coefficients involving fuzzy variables. But all the existing methods are based on the assumption that all the fuzzy coefficients and the fuzzy variables are nonnegative fuzzy numbers. In this paper a new method is proposed to solve an FFLS with arbitrary coefficients and arbitrary solution vector, that is, there is no restriction on the elements that have been used in the FFLS. The primary objective of this paper is thus to introduce the concept and a computational method for solving FFLS with no non negative constraint on the parameters. The method incorporates the principles of linear programming in solving an FFLS with arbitrary coefficients and is not only easier to understand but also widens the scope of fuzzy linear equations in scientific applications. To show the advantages of the proposed method over existing methods we solve three FFLSs.
Highlights
One field of applied mathematics that has many applications in various areas of science is solving a system of linear equations
Buckley and Qu [2] defined the concept of solving fuzzy equations and their work has been influential in the study of fuzzy linear systems
We find the solution of fully fuzzy linear systems (FFLS) as x1 = (1, 2, 2), x2 = (−3, 1, 2)
Summary
One field of applied mathematics that has many applications in various areas of science is solving a system of linear equations. Buckley and Qu [2] defined the concept of solving fuzzy equations and their work has been influential in the study of fuzzy linear systems. A general model for solving an n × n fuzzy linear system whose coefficient matrix is crisp and the right-hand side column is an arbitrary fuzzy vector was first proposed by Friedman et al [3, 4]. Later some numerical methods to solve similar systems were proposed [5] and extended methods like successive overrelaxation [6] adomian decomposition [7] were presented. The condition of crispness of the coefficient matrix makes all these methods restricted with negligible applications
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