On the Solution of a Rough Interval three-level Quadratic Programming Problem
Omar M. Saad
Department of Mathematics, Faculty of Science, Helwan University, P.O.Box 11795, Cairo, Egypt.
O. E. Emam *
Department of Information Systems, Faculty of Computers and Information, Helwan University, P.O.Box 11795, Egypt.
Marwa M. Sleem
Department of Basic Sciences, Higher Thebes Institute of Engineering, Maadi, Cairo, Egypt.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Quadratic Programming, Three-level Programming, Rough Intervals Programming