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 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.

SOME NEW COMPUTATIONAL METHODS TO SOLVE DUAL FULLY FUZZY LINEAR SYSTEM OF ARBITRARY TRIANGULAR FUZZY NUMBERS

2013 ◽  
Vol 09 (01) ◽  
pp. 13-26 ◽  
Author(s):  
AMIT KUMAR ◽  
BABBAR NEETU ◽  
ABHINAV BANSAL
Keyword(s):  
Linear System ◽  
Computational Methods ◽  
Fuzzy Numbers ◽  
Coefficient Matrix ◽  
Computational Techniques ◽  
Triangular Fuzzy Numbers ◽  
Numerical Examples ◽  
Fully Fuzzy Linear System ◽  
Fuzzy Linear System ◽  
Methods Numerical

In this paper, we discuss two new computational techniques for solving a generalized fully fuzzy linear system (FFLS) with arbitrary triangular fuzzy numbers (m,α,β). The methods eliminate the non-negative restriction on the fuzzy coefficient matrix that has been considered by almost every method in the literature and relies on the decomposition of the dual FFLS into a crisp linear system that can be further solved by a variety of classical methods. To illustrate the proposed methods, numerical examples are solved and the obtained results are discussed. The methods pose several advantages over the existing methods to solve a simple or dual FFLS.

A new method for solving an arbitrary fully fuzzy linear system

2013 ◽  
Vol 17 (9) ◽  
pp. 1725-1731 ◽  
Author(s):  
S. Moloudzadeh ◽  
T. Allahviranloo ◽  
P. Darabi
Keyword(s):  
Linear System ◽  
New Method ◽  
Fully Fuzzy Linear System ◽  
Fuzzy Linear System

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 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.

A note on “A new method for solving an arbitrary fully fuzzy linear system”

2016 ◽  
Vol 21 (23) ◽  
pp. 7117-7118
Author(s):  
Diptiranjan Behera ◽  
S. Chakraverty
Keyword(s):  
Linear System ◽  
New Method ◽  
Fully Fuzzy Linear System ◽  
Fuzzy Linear System
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