Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables

Linear programming problems with trapezoidal fuzzy variables (FVLP) have recently attracted some interest. Some methods have been developed for solving these problems by introducing and solving certain auxiliary problems. Here, we apply a linear ranking function to order trapezoidal fuzzy numbers. T...

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Bibliographic Details
Published in:Fuzzy sets and systems Vol. 158; no. 17; pp. 1961 - 1978
Main Authors: Mahdavi-Amiri, N., Nasseri, S.H.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.09.2007
Elsevier
Subjects:
Applied sciences
Circuit properties
Computer science; control theory; systems
Control theory. Systems
Digital circuits
Dual simplex
Duality
Electric, optical and optoelectronic circuits
Electronic circuits
Electronics
Exact sciences and technology
Fuzzy variable linear programming
Information, signal and communications theory
Mathematical methods
Miscellaneous
Ranking function
System theory
Telecommunications and information theory
Theoretical computing
Trapezoidal fuzzy number
Dual simplex
Duality
Ranking function
Fuzzy variable linear programming
Trapezoidal fuzzy number
Fuzzy system
Sensitivity analysis
Linear programming
Fuzzy set
Algorithm
Engineering
Simplex method
Information processing
Problem solving
ISSN:0165-0114, 1872-6801
Online Access:Get full text
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Summary:Linear programming problems with trapezoidal fuzzy variables (FVLP) have recently attracted some interest. Some methods have been developed for solving these problems by introducing and solving certain auxiliary problems. Here, we apply a linear ranking function to order trapezoidal fuzzy numbers. Then, we establish the dual problem of the linear programming problem with trapezoidal fuzzy variables and hence deduce some duality results. In particular, we prove that the auxiliary problem is indeed the dual of the FVLP problem. Having established the dual problem, the results will then follow as natural extensions of duality results for linear programming problems with crisp data. Finally, using the results, we develop a new dual algorithm for solving the FVLP problem directly, making use of the primal simplex tableau. This algorithm will be useful for sensitivity (or post optimality) analysis when using primal simplex tableaus.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2007.05.005