A new computational method to solve fully fuzzy linear systems for negative coefficient matrix

Kumar, Amit; Babbar, Neetu; Bansal, Abhinav

doi:10.1504/ijmtm.2012.047716

Cited by 7 publications

(2 citation statements)

References 22 publications

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“…In [24][25][26][27], researchers generalized methods for solving FFLS where the coefficients and the parameters are not only positive, but they also restrict the signs of coefficient or parameters only to positive or negative in one side of FFLS in an attempt to avoid the near-zero triangular fuzzy numbers in both sides of FFLS. In [28], Kumar et al obtained an exact and infinite positive solution for positive FFLS; moreover, they employed a similar technique to find a positive solution for negative FFLS in [29]. In [30], Malkawi et al proposed new matrix methods for solving a positive FFLS, the necessary and sufficient condition to have a positive solution was discussed, and their methods and results were also capable of solving left-right fuzzy linear system (LR-FLS) and FLS.…”

Section: Introductionmentioning

confidence: 99%

On the weakness of linear programming to interpret the nature of solution of fully fuzzy linear system

Malkawi

Ahmad

Ibrahim

2014

J. Uncertain. Anal. Appl.

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One of the applications of linear programing is to get solutions for fully fuzzy linear system (FFLS) when the near-zero fuzzy number is considered. This usage could be applied to interpret the nature of FFLS solution according to the nature of FFLS solution in the work of Babbar et al. (Soft Comput. 17:1-12, 2012) and Kumar et al. (Advances in Fuzzy Systems 2011:1-8, 2011). This paper shows that the nature of FFLS solutions must not depend upon the nature of linear programming (LP) solutions, because LP is not enough to obtain all the exact solutions for FFLS which contradicts the claims of researchers. Counter examples are provided in order to falsify those claims. Numerically, we confirm that the nature of the possible way of solving FFLS is completely different from that of the linear system. For instance, FFLS may have two unique solutions which contradict the uniqueness that can be obtained through only one unique solution.

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Section: Introductionmentioning

confidence: 99%

On the weakness of linear programming to interpret the nature of solution of fully fuzzy linear system

Malkawi

Ahmad

Ibrahim

2014

J. Uncertain. Anal. Appl.

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“…Also, in [9,10], Abbasbandy et al proposed the LU-decomposition method and the Steepest descent method to solve system, respectively. For more research see [11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

General Solutions of Fully Fuzzy Linear Systems

Allahviranloo

Salahshour

Homayoun-nejad

et al. 2013

Abstract and Applied Analysis

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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.

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An Algorithm for a Positive Solution of Arbitrary Fully Fuzzy Linear System

2015

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This paper proposes a new computational method to obtain a positive solution for arbitrary fully fuzzy linear system (FFLS). The new method transforms the coefficients in FFLS to a one-block matrix. As a result, none of the fuzzy operations are needed. This method can provide a solution regardless of the size of a system. Some necessary theorems are proved and new numerical examples are presented to illustrate the proposed method.

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A new computational method to solve fully fuzzy linear systems for negative coefficient matrix

Cited by 7 publications

References 22 publications

On the weakness of linear programming to interpret the nature of solution of fully fuzzy linear system

On the weakness of linear programming to interpret the nature of solution of fully fuzzy linear system

General Solutions of Fully Fuzzy Linear Systems

An Algorithm for a Positive Solution of Arbitrary Fully Fuzzy Linear System

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