scholarly journals A New Approach for Solving Fully Fuzzy Linear Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Amit Kumar ◽  
Neetu ◽  
Abhinav Bansal
Keyword(s):  
Linear Systems ◽  
Fuzzy Numbers ◽  
Linear Equations ◽  
Primary Objective ◽  
Computational Method ◽  
Solution Vector ◽  
New Approach ◽  
Fuzzy Variables ◽  
Fuzzy Linear System ◽  
Fuzzy Linear Systems

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.

scholarly journals A QUADRATIC PROGRAMMING MODEL FOR OBTAINING WEAK FUZZY SOLUTION TO FUZZY LINEAR SYSTEMS

2019 ◽  
pp. 381
Author(s):  
Abbas Akrami ◽  
Majid Erfanian
Keyword(s):  
Experimental Data ◽  
Linear Systems ◽  
Optimization Model ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Linear Equations ◽  
Real Life ◽  
System Of Linear Equations ◽  
Fuzzy Solution ◽  
Fuzzy Linear Systems

Real life applications arising in various fields of engineering and science (e.g. electrical, civil, economics, dietary, etc.) can be modelled using a system of linear equations. In such models, it may happen that the values of the parameters are not known or they cannot be stated precisely and that only their estimation due to experimental data or experts knowledge is available. In such a situation it is convenient to represent such parameters by fuzzy numbers. In this paper we propose an efficient optimization model for obtaining a weak fuzzy solution to fuzzy linear systems (FLS). We solve some examples and we show that this method is always efficient.

scholarly journals Software for Solving Fully Fuzzy Linear Systems with Rectangular Matrix

2020 ◽  
Vol 10 (1) ◽  
pp. 129-139
Author(s):  
A.V. Panteleev ◽  
V.S. Saveleva
Keyword(s):  
Linear Systems ◽  
Linear Equations ◽  
Linear System Of Equations ◽  
Software Application ◽  
Rectangular Matrix ◽  
Fuzzy Linear System ◽  
Triangular Numbers ◽  
Systems Of Linear Equations ◽  
The Mean ◽  
Fuzzy Linear Systems

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.

scholarly journals An Application of Interval Arithmetic for Solving Fully Fuzzy Linear Systems with Trapezoidal Fuzzy Numbers

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Esmaeil Siahlooei ◽  
Seyed Abolfazl Shahzadeh Fazeli
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Interval Arithmetic ◽  
Fuzzy Numbers ◽  
New Method ◽  
Numerical Examples ◽  
Fully Fuzzy Linear System ◽  
Basic Interval ◽  
Fuzzy Linear System ◽  
Fuzzy Linear Systems

We present a method for solving fully fuzzy linear systems using interval aspects of fuzzy numbers. This new method uses a decomposition technique to convert a fully fuzzy linear system into two types of decomposition in the form of interval matrices. It finds the solution of a fully fuzzy linear system by using interval operations. This new method uses interval arithmetic and two new interval operations ⊖ and ⊘. These new operations, which are inverses of basic interval operations + and ×, will be presented in the middle of this paper. Some numerical examples are given to illustrate the ability of proposed methods.

scholarly journals H-Matrices in Fuzzy Linear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
H. Saberi Najafi ◽  
S. A. Edalatpanah
Keyword(s):  
Linear System ◽  
Theoretical Analysis ◽  
Linear Systems ◽  
Numerical Experiments ◽  
Coefficient Matrix ◽  
System Of Equations ◽  
Linear System Of Equations ◽  
Fuzzy Linear System ◽  
Fuzzy Linear Systems

We consider a class of fuzzy linear system of equations and demonstrate some of the existing challenges. Furthermore, we explain the efficiency of this model when the coefficient matrix is an H-matrix. Numerical experiments are illustrated to show the applicability of the theoretical analysis.

scholarly journals General Solutions of Fully Fuzzy Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
T. Allahviranloo ◽  
S. Salahshour ◽  
M. Homayoun-nejad ◽  
D. Baleanu
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Solution Set ◽  
Solution Sets ◽  
General Solutions ◽  
Fully Fuzzy Linear System ◽  
Fuzzy Linear System ◽  
Fuzzy Linear Systems

We propose a method to approximate the solutions of fully fuzzy linear system (FFLS), the so-calledgeneral solutions. So, we firstly solve the 1-cut position of a system, then some unknown spreads are allocated to each row of an FFLS. Using this methodology, we obtain some general solutions which are placed in the well-known solution sets like Tolerable solution set (TSS) and Controllable solution set (CSS). Finally, we solved two examples in order to demonstrate the ability of the proposed method.

scholarly journals A New Approach for Solving Type-2-Fuzzy Transportation Problem

2019 ◽  
Vol 4 (3) ◽  
pp. 683-696
Author(s):  
Somnath Maity ◽  
Sankar Kumar Roy
Keyword(s):  
Transportation Problem ◽  
Original Problem ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Simplex Algorithm ◽  
New Approach ◽  
Fuzzy Variables ◽  
Linear Programming Problems ◽  
Fuzzy Transportation Problem

In this paper, a new approach is introduced to solve transportation problem with type-2-fuzzy variables. In most of the real-life situations, the available data do not happen to be crisp in nature. It gives rise to the fuzzy transportation problem (FTP). This proposed approach concentrates on the problem when the vertical slices of type-2-fuzzy sets (T2FSs) are trapezoidal fuzzy numbers (TFNs). The original problem reduces to three different linear programming problems (LPPs) which are solved using the simplex algorithm. Then the effectiveness of this paper is discussed with numerical example. In conclusion, the significance of the paper and the scope of future study are discussed.

scholarly journals A note on “The nearest symmetric fuzzy solution for a symmetric fuzzy linear system”

2015 ◽  
Vol 23 (2) ◽  
pp. 173-177 ◽  
Author(s):  
Ghassan Malkawi ◽  
Nazihah Ahmad ◽  
Haslinda Ibrahim
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Approximate Solutions ◽  
Fuzzy Linear System ◽  
Fuzzy Solution ◽  
Fuzzy Linear Systems

Abstract This paper provides accurate approximate solutions for the symmetric fuzzy linear systems in (Allahviranloo et al:[1]).

scholarly journals Fully Fuzzy Linear Systems in Python Programming

2020 ◽  
Vol 9 (4) ◽  
pp. 951-956
Keyword(s):  
Linear System ◽  
Fuzzy Number ◽  
Symmetric Matrix ◽  
Triangular Matrix ◽  
New Approach ◽  
Numerical Examples ◽  
Fuzzy Matrix ◽  
Fuzzy Linear System ◽  
Python Programming ◽  
Fuzzy Linear Systems

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.

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