On the Solution of a Rough Interval three-level Quadratic Programming Problem

In this paper, a three-level quadratic programming (QP) problem is considered where some or all of its coefficients in the objective function are rough intervals. At the first phase of the solution approach and to avoid the complexity of the problem, two QP problems with interval coefficients will be formulated. One of these problems is a QP where all of its coefficients are upper approximation of rough intervals and the other problem is a QP where all of its coefficients are lower approximations of rough intervals. At the second phase, a membership function is constructed to develop a fuzzy model for obtaining the optimal solution of the three-level quadratic programming problem. Finally, an illustrative numerical example is given to demonstrate the obtained results.