Solving Fuzzy Linear Programming Problem by Interior Point Method

In this article we consider a linear programming problem where the objectives are fuzzy functions (fuzzyvalued functions). various methods have been developed for solving linear programming problems with fuzzy number, such as simplex method and dual simplex method. But theircomputational complexities are exponential, which is not satisfactory for solving largescale fuzzy linear programming problems, especially in the engineering field.A new method which can solve large-scale fuzzy number linear programming problems is presented in this paper,which is named a revised interior pointmethod. Its idea is similar to that of interior pointmethod used for solving linear programming problems in crisp environment before, but its feasible direction and step size are chosen by using trapezoidal fuzzy numbers, linear ranking function, fuzzy vector, and their operations.

Keywords:

Fuzzy linear programming , Interior point method , Ranking function