New Methods For Solving Imprecisely Defined Linear Programming Problem Under Trapezoidal Fuzzy Uncertainty

In this paper, imprecisely defined linear programming problem under fuzzy uncertainty has taken into consideration for the analysis. Accordingly, in the considered problem, elements of the coefficient matrix of the constraints and coefficients of the objective functions are assumed as crisp. However, decision variables and the right-hand side vector of the constraints are anticipated as uncertain in nature. Uncertainty presents in the problem are modelled through convex normalized trapezoidal fuzzy sets. In this regard, two new methods have been proposed for the solution using the concept of fuzzy centre and radius. For the first method, coefficients are considered as non-negative, whereas mixed i.e., both non-negative and negative coefficients are considered for the second method. The advantages of the proposed methods over some existing methods such as Mahdavi-Amiri and Nasseri (2007) and Saati et al. (2015), are discussed. In special cases, the results are compared with some the mentioned methods and some numerical examples are given.