Solutions of Fuzzy System of Linear Equations

Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures - Advances in Computer and Electrical Engineering ◽

10.4018/978-1-7998-0190-0.ch002 ◽

2020 ◽

pp. 26-33

Author(s):

Laxminarayan Sahoo

Keyword(s):

Linear System ◽

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Fuzzy Number ◽

Fuzzy System ◽

Linear Equations ◽

System Of Linear Equations ◽

Interval System ◽

Solution Methodology

This chapter deals with solution methodology of fuzzy system of linear equations (FSLEs). In fuzzy set theory, finding solutions of FLSEs has long been a well-known problem to the researchers. In this chapter, the fuzzy number has been converted into interval number, and the authors have solved the interval system of linear equation for finding the fuzzy valued solution. Here, a fuzzy valued linear system has been introduced and a numerical example has been solved and presented for illustration of purpose.

Download Full-text

A Novel Technique to Solve the Fuzzy System of Equations

Mathematics ◽

10.3390/math8050850 ◽

2020 ◽

Vol 8 (5) ◽

pp. 850

Author(s):

Nasser Mikaeilvand ◽

Zahra Noeiaghdam ◽

Samad Noeiaghdam ◽

Juan J. Nieto

Keyword(s):

Linear System ◽

Fuzzy Number ◽

Fuzzy System ◽

Linear Equations ◽

Second Step ◽

Negative Solution ◽

System Of Linear Equations ◽

Vector Solution ◽

Novel Technique ◽

Fuzzy Linear System

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.

Download Full-text

Certain efficient iterative methods for bipolar fuzzy system of linear equations

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-200084 ◽

2020 ◽

Vol 39 (3) ◽

pp. 3971-3985 ◽

Cited By ~ 3

Author(s):

Muhammad Saqib ◽

Muhammad Akram ◽

Shahida Bashir

Keyword(s):

Approximate Solution ◽

Linear System ◽

Iterative Methods ◽

Fuzzy Set ◽

Fuzzy System ◽

Linear Equations ◽

Performance Validity ◽

System Of Linear Equations ◽

Numerical Examples ◽

Iterative Schemes

A bipolar fuzzy set model is an extension of fuzzy set model. We develop new iterative methods: generalized Jacobi, generalized Gauss-Seidel, refined Jacobi, refined Gauss-seidel, refined generalized Jacobi and refined generalized Gauss-seidel methods, for solving bipolar fuzzy system of linear equations(BFSLEs). We decompose n × n BFSLEs into 4n × 4n symmetric crisp linear system. We present some results that give the convergence of proposed iterative methods. We solve some BFSLEs to check the validity, efficiency and stability of our proposed iterative schemes. Further, we compute Hausdorff distance between the exact solutions and approximate solution of our proposed schemes. The numerical examples show that some proposed methods converge for the BFSLEs, but Jacobi and Gauss-seidel iterative methods diverge for BFSLEs. Finally, comparison tables show the performance, validity and efficiency of our proposed iterative methods for BFSLEs.

Download Full-text

THE SERIES OF FUZZIFIED FUZZY BEZIER CURVE

Jurnal Teknologi ◽

10.11113/jt.v78.6935 ◽

2015 ◽

Vol 78 (2-2) ◽

Author(s):

Rozaimi Zakaria ◽

Abd. Fatah Wahab ◽

R. U. Gobithaasan

Keyword(s):

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Fuzzy Number ◽

Bézier Curve ◽

Bezier Curve ◽

Bezier Curves ◽

Number Concepts ◽

Bézier Curves

This paper discusses about the series of fuzzified Bezier curves. This series of fuzzified Bezier curves constructed based on the fuzzy set theory especially fuzzy number concepts. The series of fuzzified represented by the alpha-cut of fuzzy number with various values of alpha. Then, the results were blended with Bezier curve function to produce the series of fuzzified fuzzy Bezier curves.

Download Full-text

A Proposed Method for Solving Fuzzy System of Linear Equations

The Scientific World JOURNAL ◽

10.1155/2014/782093 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Reza Kargar ◽

Tofigh Allahviranloo ◽

Mohsen Rostami-Malkhalifeh ◽

Gholam Reza Jahanshaloo

Keyword(s):

Linear Programming ◽

Linear System ◽

Programming Problem ◽

Fuzzy System ◽

Linear Programming Problem ◽

Linear Equations ◽

System Of Linear Equations ◽

Numerical Examples ◽

Interval Solution ◽

Practical Algorithm

This paper proposes a new method for solving fuzzy system of linear equations with crisp coefficients matrix and fuzzy or interval right hand side. Some conditions for the existence of a fuzzy or interval solution ofm×nlinear system are derived and also a practical algorithm is introduced in detail. The method is based on linear programming problem. Finally the applicability of the proposed method is illustrated by some numerical examples.

Download Full-text