Fuzzy Primal and Dual Simplex Algorithms for Solving Fuzzy Linear Programming Problems by Use of Ranking Functions

Fuzzy linear programming (FLP) problems have recently attracted much interest. We have established duality results for two classes of fuzzy problems [1]: (1) fuzzy number linear programming (FNLP) problems,and (2) linear programming with fuzzy variables (FVLP) problems. For each problem, the weak duality, strong duality and their correspondingresults and, in particular, the complementary slackness theorem is proved. For the FVLP problems, we show that the auxiliary problem, recentlyintroduced in the literature, is indeed dual of the FVLP problem. We consider both problems using fuzzy trapezoidal numbers and variables.We explain both the primal and dual simplex algorithms based on theprimal tableau for the FNLP and FVLP problems. These algorithmswould be useful in performing sensitivity analysis for both classes ofproblems.

Keywords:

Duality , fuzzy linear programming , ranking function , trapezoidal fuzzy number