A Novel Technique to Solve the Fuzzy System of Equations

The aim of this research is to apply a novel technique based on the embedding method to solve the n × n fuzzy system of linear equations (FSLEs). By using this method, the strong fuzzy number solutions of FSLEs can be obtained in two steps. In the first step, if the created n × n crisp linear system has a non-negative solution, the fuzzy linear system will have a fuzzy number vector solution that will be found in the second step by solving another created n × n crisp linear system. Several theorems have been proved to show that the number of operations by the presented method are less than the number of operations by Friedman and Ezzati’s methods. To show the advantages of this scheme, two applicable algorithms and flowcharts are presented and several numerical examples are solved by applying them. Furthermore, some graphs of the obtained results are demonstrated that show the solutions are fuzzy number vectors.

Fully Fuzzy Linear Systems in Python Programming

This paper proposes the python coding for ST decomposition for Triangular, Trapezoidal, and computing the algorithms for the fully fuzzy linear system in python programming. where is a fuzzy matrix, are fuzzy vectors. ST decompose into a product of symmetric matrix (S) and triangular matrix (T) in the form of triangular and trapezoidal fuzzy number matrices. To best illustrate the proposed methods by python coding algorithm with a new approach Python coding has been adopted. Algorithms have been introduced and the numerical examples have been solved by using python techniques. A study of ST decomposition have been done and the solution is obtained with different algorithms. New numerical problems are presented and an example has been solved for this algorithms and the solutions are obtained.

Software for Solving Fully Fuzzy Linear Systems with Rectangular Matrix

The article discusses the problem of solving a fully fuzzy linear system of equations with a fuzzy rectangular matrix and a fuzzy right-hand side described by fuzzy triangular numbers in a form of deviations from the mean. A solution algorithm based on finding pseudo-solutions of systems of linear equations and corresponding software is formed. Various examples of created software application for arbitrary fuzzy linear systems are given.

Iterative Methods for Solving a System of Linear Equations in a Bipolar Fuzzy Environment

We develop the solution procedures to solve the bipolar fuzzy linear system of equations (BFLSEs) with some iterative methods namely Richardson method, extrapolated Richardson (ER) method, Jacobi method, Jacobi over-relaxation (JOR) method, Gauss–Seidel (GS) method, extrapolated Gauss-Seidel (EGS) method and successive over-relaxation (SOR) method. Moreover, we discuss the properties of convergence of these iterative methods. By showing the validity of these methods, an example having exact solution is described. The numerical computation shows that the SOR method with ω = 1 . 25 is more accurate as compared to the other iterative methods.