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

Mahdavi Amiri, N ; Sharif University of Technology | 2007

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  1. Type of Document: Article
  2. DOI: 10.1016/j.fss.2007.05.005
  3. Publisher: 2007
  4. Abstract:
  5. 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. © 2007 Elsevier B.V. All rights reserved
  6. Keywords:
  7. Algorithms ; Function evaluation ; Linear programming ; Number theory ; Problem solving ; Dual simplex ; Fuzzy variable linear programming ; Ranking function ; Trapezoidal fuzzy number ; Fuzzy sets
  8. Source: Fuzzy Sets and Systems ; Volume 158, Issue 17 , 2007 , Pages 1961-1978 ; 01650114 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0165011407002163