A dual simplex method for bounded linear programmes with fuzzy numbers

Fuzzy number linear programming problems have recently attracted some interests. Some authors used the concept of comparison of fuzzy numbers for solving fuzzy linear programming problems. In effect, most convenient methods are based on the concept of comparison of fuzzy numbers by use of ranking functions. But the existing methods are not useful for situations in which some or all variables are restricted to lie within fuzzy lower and fuzzy upper bounds. In this paper, we introduce a new method called the bounded dual simplex method for bounded fuzzy number linear programming problems which is useful for these situations. This algorithm constructs a dual feasible basic solution after obtaining a working basic and from there moves towards attaining primal feasibility while maintaining dual feasibility throughout.

bounded linear programming, FNLP, fuzzy number linear programming, fuzzy ordering, TRFNs, trapezoidal fuzzy numbers