In this paper, a multi- objective quadratic programming (Poss- MOQP) problem with possibilistic variables coefficients matrix in the objective functions is studied. Through the use of level sets the Poss- MOQP problem is converted into the corresponding deterministic multi- objective quadratic programming ( MOQP) problem and hence into the single parametric quadratic programming problem using the weighting method. An extended possibly efficient solution is specified. A necessary and sufficient condition for finding such a solution is established. A relationship between the solutions of possibilistic levels is constructed. Numerical example is given in the sake for the paper to clarify the obtained results.

Ammar,E.E., and Khalifa, H.A. (2003). Fuzzy portfolio selection problem- quadratic programming approach. Chaos, Solitons and Fractels, Vol. 18(5), pp. 1045-1054.

Ammar, E. E. (2008). On solutions of fuzzy random multiobjective quadratic programming with application in portfolio problem. Information Sciences, Vol. 178(2), pp. 468-484.

Ammar,E.E., and Khalifa, H.A. (2015). On rough interval quadratic programming approach for minimizing the total variability in the future payments to portfolio selection problem. International Journal of Mathematical Archive, Vol. 6(1), pp. 67-75.

Bazaraa, M. S., Jarvis, J. J., and Sherall, H. D. (1990). Linear Programing and Network Flows, Jon& Wiley, New York. Canestrelli, E., Giove, S., and Fuller, R. (1996). Stability in possibilistic quadratic programming. Fuzzy Sets and Systems, Vol. 82(1), pp. 51-56.

Dubois, D., and Prade, H. (1980). System for linear fuzzy constraints. Fuzzy Sets and Systems, Vol. 3, pp. 37- 48. Horst, R., and Tuy, H. (1993). Global Optimization: Deterministic Approach. Berlin: Springer- Verlage.

Hussein, M. L. (1992). On convex vector optimization problems with possibilistic weights. Fuzzy Sets and Systems, Vol. 51, pp. 289- 294.

Inuiguchi, M., and Ramik, J. (2000). Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets and Systems, Vol. 111(1), pp. 3-28.

Jana, P., Roy, T.K., and Mazunder, S. K. (2009). Multi- objective possibilities model for portfolio selection with transaction cost. Journal of Computational and Applied Mathematics, Vol. 228, pp. 188-196.

Kassem, M.A. (1998). Stability of possibilistic multiobjective nonlinear programming problems without differentiability. Fuzzy Sets and Systems, Vol. 94, pp. 239-246.

Khalifa, H. A., and ZeinEldein, R. A. (2014). Fuzzy programming approach for portfolio selection roblems with fuzzy coefficients. International Journal of Scientific Knowledge. Vol. 4(7), pp. 40-47.

Khalifa, H. A. (2016). An interactive approach for solving fuzzy multiobjective nonlinear programming problems. Journal of Mathematics, Vol. 24(3), pp. 535-545.

Kheirfam, B. (2011). A method for solving fully fuzzy quadratic programming problems. Acta Universitatis Apulensis, Vol. 27, pp. 69-76.

Luhandjula, M. K. (1987). Multiple objective programming problems with possibilistic coefficients. Fuzzy Sets and Systems, Vol. 21, pp. 135-145.

Miettinen, K.M. (1999). Nonlinear Multiobjective Optimization. Kulwer A cademic Publishers.

Narula, C. S., L. Kirilov and V. Vassiley (1993). An Interactive Algorithm for Solving Multiple Objective Nonlinear Programming Problems, Multiple Criteria Decision Making, and Proceeding of the tenth International Conference: Expand and Enrich the Domain of Thinking and Application, Berlin: Springer Verlag.

Pardalos, P. M., and Rosen, J. B. (1987). Constrained global optimization: Algorithms and Applications. Lecture notes in Computer Science, volume 268, Berlin: Springer- Verlage.

Sakawa, M., and Yano, H. (1989). Interactive decision making for multiobjective nonlinear programming problems with fuzzy parameters. Fuzzy Sets and Systems, Vol. 29, pp. 315-326.

Steuer, R. E. (1983). Multiple Criteria Optimization: Theory, Computation and Application, New York: Jon & Wiley.

Tanaka, H., Guo, P., and Zimmerman, H- J. (2000). Possibility distributions of fuzzy decision variables obtained from possibilistic linear programming problems. Fuzzy Sets and Systems, Vol. 113, pp. 323-332.

Wang, M. X., Z. L. Qin and Y. D. Hu (2001). An interactive algorithm for solving multicriteria decision making: the attainable reference point method, IEEE Transaction on Systems, Man, and Cybernetics- part A : Systems and Humans, Vol. 31(3), pp.194-198.

Zadeh, L. A. (1965). Fuzzy sets. Information Control, Vol. 8, pp. 338-353.

Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, Vol. 1, pp. 3-28.