Some New Results in Linear Programming Problems with Fuzzy Cost Coefficients

The fuzzy primal simplex method proposed by Mahdavi-Amiri et al. and the fuzzy dual simplex method proposed by SH Nasseri and A Ebrahimnejad are two current procedures for solving linear programming problems with fuzzy cost coefficients known as reduced fuzzy numbers linear programming (RFNLP) probl...

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Bibliographic Details
Published in:	Walailak journal of science and technology Vol. 10; no. 2
Main Author:	Ali EBRAHIMNEJAD
Format:	Journal Article
Language:	English
Published:	Walailak University 01.04.2013
Subjects:	fuzzy dual simplex algorithm Fuzzy numbers linear programming fuzzy primal simplex algorithm trapezoidal fuzzy number
ISSN:	1686-3933, 2228-835X
Online Access:	Get full text
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Summary:	The fuzzy primal simplex method proposed by Mahdavi-Amiri et al. and the fuzzy dual simplex method proposed by SH Nasseri and A Ebrahimnejad are two current procedures for solving linear programming problems with fuzzy cost coefficients known as reduced fuzzy numbers linear programming (RFNLP) problems. In this paper, we prove that in the absence of degeneracy these fuzzy methods stop in a finite numbers of iterations. We also prove the fundamental theorem of linear programming in a crisp environment to a fuzzy one. Finally, we illustrate our proof by use of a numerical example.
ISSN:	1686-3933 2228-835X
DOI:	10.2004/wjst.v10i2.424