“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 8558
School of Mathematics
  Title:   Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables
  Author(s):  N. Mahdavi-Amiri (Joint with S. H. Nasseri)
  Status:   Published
  Journal: Fuzzy Sets and Systems
  Vol.:  158
  Year:  2007
  Pages:   1961-1978
  Supported by:  IPM
Linear programming problems with trapezoidal fuzzy variables (FVLP) have recently attracted some interest. Some methods have been de�veloped 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 re�sults. 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.

Download TeX format
back to top
scroll left or right