Solution of the Generalized Interval Linear Programming Problems: Pessimistic and Optimistic Approaches

Abstract

This paper deals with linear programming problem with interval numbers as coefficients to exhibit with uncertainty. Since, the set of common intervals is not a field, we define generalized interval numbers to produce an algebraic interval field and on this field, we propose principle of uncertainty traverse instead of extension principle which permits to define operators on intervals exactly similar to the same operators on real numbers. In addition, we apply a total order on this field to transform interval linear programming into a traditional problem. The proposed order can be extended either pessimistically or optimistically. The numerical experiments are given to demonstrate the efficiency of the proposed scheme in comparison with the previous established works. The approach in this paper can be generalized to fuzzy linear programming problems taking the fuzzy cuts into account.