Abstract
In recent years various attempts have been made to study the solution of fuzzy variable linear programming problems by introducing and solving certain auxiliary problems or directly by the use of dual simplex method based on a certain linear ranking function. But these methods are not applicable for situations in which some or all variables are restricted to lie within fuzzy lower and fuzzy upper bounds. In this paper, as a natural extension of the results in crisp linear programming and based on a certain linear ranking function we obtain some new results leading to a new method to overcome this shortcoming. To show the application of our method a real life problem is solved by using the proposed method. Also, one application of this approach in solving maximum flow problem with fuzzy capacity is dealt with.