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) 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.

Fuzzy numbers linear programming, fuzzy primal simplex algorithm, fuzzy dual simplex algorithm, trapezoidal fuzzy number