Method to Solve Linear Programming Problems Using Vague Sets

In the process of finding the solutions of real life problems decision makers always remain in confusion that the data they are using to solve there problems are exact or not. In solving a linear programming problem, optimize Z = C^T x subject to (Ax)_i les b_i, foralli, x ges 0 there may be confusion about the values of c^T, b_i and A and due to confusion for these values the confusion may also exist for the value of objective function. Several researchers have used fuzzy set theory for linear programming problems but this theory could not tackle the confusion part of the data. There is no method in the literature for solving linear programming problems in the situation when decision makers are in confusion about the exactness of the data. To incorporate this confusion concept of vague sets have been used. In this paper, we have extended the idea of fuzzy linear programming by vague linear programming and proposed a new method to solve linear programming problems by assuming that the decision makers are confused only for the values of b_i and there is no confusion and uncertainty for the values of c^T and A . To explain the advantage of proposed method, a numerical example is solved. Obtained results are explained.