General Fuzzy Linear Systems Research Articles

Linear System Of Equations With Trapezoidal Fuzzy Numbers

A general fuzzy linear system of equations is investigated using embedding approach. In the literature of fuzzy systems two types of linear systems are more important: 1) Fuzzy Linear Systems, 2) Fully Fuzzy Linear Systems. In both class of these systems usually the authors considered triangular type of fuzzy numbers. In this paper, we introduce a linear system of equations with trapezoidal fuzzy numbers as an extension of the fuzzy linear systems which was first introduced by Friedman et al. [6]. Conditions for the existence of a trapezoidal fuzzy solution to n×n linear system are derived and a numerical procedure for calculating the solution is illustrated with some examples.

Bounded and symmetric solutions of fully fuzzy linear systems in dual form

Abstract Linear systems have important applications in many branches of science and engineering in many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. So, it is immensely important to develop a numerical procedure that would appropriately treat general fuzzy linear systems and solve them. In this paper, we propose bounded and symmetric solutions of fully fuzzy linear systems in the dual form (DFFLS) based on a 1-cut expansion. To this end, we solve the 1-cut of a DFFLS (we assumed that the 1-cut of a DFFLS is a crisp linear system), then some unknown symmetric spreads are allocated to each row of a 1-cut of a DFFLS. So, after some manipulations, the original DFFLS is transformed to solving 2∗ n linear equations to find the symmetric spreads. However, our method always give us a fuzzy vector solution. Moreover, we show that the bounded and symmetric solution of the DFFLS will be placed in the tolerable solution set (TSS) and in the controllable solution set (CSS), respectively. Also, an economic example is solved to illustrate the ability of proposed method and a new pattern is suggested for comparing the obtained solutions.

Solving fuzzy linear systems

In this paper, the main aim is to develop a method for solving an arbitrary general fuzzy linear system by using the embedding approach. Considering the existing and uniqueness of fuzzy solution to n × n linear fuzzy system is done. Numerical examples are presented to illustrate the proposed model.

Solution to General Fuzzy Linear System and Its Necessary and Sufficient Condition

This paper investigates general fuzzy linear systems of the form Ax = y and general dual fuzzy linear systems of the form Ax + y = Bx + z with A, B matrices of crisp coefficients and x, y fuzzy number vectors. The aim of this paper is twofold. First, by the unique least Euclidean norm solution we solve the systems with non-full rank matrices A, B. Second, we give the new necessary and sufficient condition for a strong fuzzy solution existence. Moreover, some numerical examples are designed.

Linear Formed General Fuzzy Linear Systems

Abstract According to the structured element method, the article investigates a method of solving the general fuzzy linear systems and dual general fuzzy linear systems, which are linear formed by fuzzy structured element, and gives the necessary and sufficient condition for the existence of a fuzzy solution. At the same time, some examples in engineering and economics are designed.

Numerical Solving of General Fuzzy Linear Systems by Huang's Method

Numerical Solving of General Fuzzy Linear Systems by Huang's Method

Numerical Solving of General Fuzzy Linear Systems by Huang's Method

Numerical Solving of General Fuzzy Linear Systems by Huang's Method

Iterative solution of fuzzy linear systems

Linear systems have important applications to many branches of science and engineering. In many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. So it is immensely important to develop numerical procedures that would appropriately treat general fuzzy linear systems (will be denoted by FLS) and solve them. In this paper firstly a general fuzzy linear system using the embedding approach, has been investigated and then several well-known numerical algorithms for solving system of linear equations such as Richardson, Extrapolated Richardson, Jacobi, JOR, Gaus †–Seidel, EGS, SOR, AOR, ESOR, SSOR, USSOR, EMA and MSOR are extended for solving FLS. The iterative methods are followed by convergence theorems and the presented algorithms are tested by solving some numerical examples. ( †Hackbusch noticed that Gauss spelling is less correct than Gaus [W. Hackbusch, Iterative Solution of Large Sparse Systems of Equations, Springer-Verlag Inc., New York, 1994 [9]].)

Fuzzy linear systems

A general fuzzy linear system is investigated using the embedding approach. Conditions for the existence of a unique fuzzy solution to n × n linear system are derived and a numerical procedure for calculating the solution is designed. The applicability of the proposed model is illustrated with examples.