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On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem. (English) Zbl 1149.90188

Summary: In this paper, a multiobjective quadratic programming problem fuzzy random coefficients matrix in the objectives and constraints and the decision vector are fuzzy variables is considered. First, we show that the efficient solutions fuzzy quadratic multiobjective programming problems series-optimal-solutions of relative scalar fuzzy quadratic programming. Some theorems are to find an optimal solution of the relative scalar quadratic multiobjective programming with fuzzy coefficients, having decision vectors as fuzzy variables. An application fuzzy portfolio optimization problem as a convex quadratic programming approach is discussed and an acceptable solution to such problem is given. At the end, numerical examples are illustrated in the support of the obtained results.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
91B28 Finance etc. (MSC2000)
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[1] B. Alidaee, F. Glover, G. Kochenberger, H. Wang, Solving the maximum edge weight clique problem via unconstrained quadratic programming, Eur. J. Oper. Res. 2006 (Available Online 7 September). · Zbl 1131.90046
[2] Ammar, E.; Khalifa, H.A., Fuzzy portfolio optimization a quadratic programming approach, Chaos solitons fractals, 18, 5, 1045-1054, (2003) · Zbl 1068.91025
[3] Bazaraa, S., Non linear programming, theory and algorithms, (1979), John Wiley & Sons New York · Zbl 0476.90035
[4] Bapistella, A.; Ollero, A., Fuzzy methodologies for interactive multicriteria optimization, IEEE trans. system man. cybernet., 10, 355-365, (1980) · Zbl 0442.90088
[5] Bellman, R.; Zadeh, L., Decision-making in a fuzzy environment, Manage. sci., 17, 141-164, (1970) · Zbl 0224.90032
[6] Cambini, R.; Carosi, L., On generalized linearity of quadratic fractional functions, J. global opt., 30, 235-251, (2004) · Zbl 1066.90088
[7] Çelikyurt, U.; Özekici, S., Multiperiod portfolio optimization models in stochastic markets using the mean – variance approach, Eur. J. oper. res., 179, 1, 186-202, (2007) · Zbl 1163.91375
[8] Chanas, S., The use of parametric programming in fuzzy linear programming, Fuzzy sets syst., 20, 17-30, (1980)
[9] Czerwik, S.; Dłutek, K., Stability of the quadratic functional equation in Lipschitz spaces, J. math. anal. appl., 293, 1, 79-88, (2004) · Zbl 1052.39030
[10] Dembo, R.S.; Rosen, D., The practice of portfolio replication: a practical overview of forward and inverse problem, Ann. oper. res., 85, 267-284, (1999) · Zbl 0920.90006
[11] K. Ding, N.-J. Huang, A new class of interval projection neural networks for solving interval quadratic program, Chaos, Solitons & Fractals, in press. · Zbl 1137.90020
[12] D. Dubois, H. Prade, Fuzzy Sets and Systems; Theory and Applications, New York, London, Toronto 1980. · Zbl 0444.94049
[13] Ehrgott, M., Mulicriteria optimization, (2005), Springer Berlin
[14] Ekel, P.Ya.; Fernando, H.S.N., Algorithms of discrete optimization and their application to problems with fuzzy coefficients, Inform. sci., 176, 846-2868, (2006) · Zbl 1141.90588
[15] J. Fliege, A. Heseler, Constructing approximations to the efficient set of convex quadratic multiobjective problems, Fachbereich Mathematik, Uni. Dortmund, 44221 Dortmund, Germany, January 7 2002.
[16] Kaufmann, A.; Cupta, M., Fuzzy mathematical models in engineering and many science, (1988), North Holland Amsterdam
[17] Kazi, S.N.R.; Sam, K.; Man, K.F., A real-coding jumping gene genetic algorithm (RJGGA) for multiobjective optimization, Inform. sci., 177, 632-654, (2007) · Zbl 1142.68524
[18] Len, T.; Vercher, E., Solving a class of fuzzy linear programs by using semi-infinite programming techniques, Fuzzy sets syst., 146, 2, 235-252, (2004) · Zbl 1061.90122
[19] Li, C.; Liao, X.; Yu, J., Tabu search for fuzzy optimization and applications, Inform. sci., 158, 3-13, (2004) · Zbl 1049.90143
[20] Li, D.F., An approach to fuzzy multiattribute decision making under uncertainty, Inform. sci, 169, 1-2, 97-112, (2005) · Zbl 1101.68840
[21] Liu, L.; Li, Y., The fuzzy quadratic assignment problem with penalty: new models and genetic algorithm, Math. comput., 174, 2, 1229-1244, (2006) · Zbl 1111.90066
[22] Liu, Y.-K.; Liu, B., A class of fuzzy random optimization: expected value models, Inform. sci., 155, 1-2, 89-102, (2003) · Zbl 1039.60002
[23] Liu, Y.-K.; Liu, B., Fuzzy random programming with equilibrium chance constraints, Inform. sci., 170, 363-395, (2005) · Zbl 1140.90520
[24] Luhandjula, M.K.; Gupta, M.M., On fuzzy stochastic optimization, Fuzzy sets syst., 81, 1, 47-55, (1996) · Zbl 0879.90187
[25] Luhandjula, M.K., Fuzziness and randomness in an optimization framework, Fuzzy sets syst., 77, 3, 291-297, (1996) · Zbl 0869.90081
[26] Masaaki, I., Efficient solution generation for multiple objectives linear programming based on extreme ray generation method, Eur. J. oper. res., 160, 1, 242-251, (2005) · Zbl 1067.90148
[27] Qiao, Z.; Wang, G., On solutions and distribution problems of the linear programming with fuzzy random variables coefficients, Fuzzy sets syst., 58, 155-170, (1993) · Zbl 0813.90127
[28] Qiao, Z.; Zhang, Y.; Wang, G., On fuzzy random linear programming, Fuzzy sets syst., 65, 31-49, (1994) · Zbl 0844.90112
[29] Sakawa, M.; Yanu, H., An interactive fuzzy satisfying method for multiobjective linear programming problems with random variable coefficients through a probability maximization model, Fuzzy sets syst., 146, 2, 205-220, (2004) · Zbl 1061.90124
[30] Sengupta, A.; Kumar Pal, T.; Chakraborty, D., Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming, Fuzzy sets syst., 119, 1, 129-138, (2001) · Zbl 1044.90534
[31] Sengupta, A.; Kumar Pal, T., On comparing interval numbers, Eur. J. oper. res., 28-43, (2000) · Zbl 0991.90080
[32] Tang, J.; Wang, D., An interactive approach based on a genetic algorithm for a type of quadratic programming problems with fuzzy objective and resources, Comput. oper. res., 24, 5, 413-422, (1997) · Zbl 0882.90128
[33] Tanaka, H.; Ishibuchi, H., Identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters, Fuzzy sets syst., 41, 2, 145-160, (1991) · Zbl 0734.62072
[34] Wang, W.; Qiao, Z., Linear programming with fuzzy random variables coefficients, Fuzzy sets syst., 57, 295-311, (1993) · Zbl 0791.90072
[35] Wan, Z.; Wu, S.Y.; Teo, K.L., Some properties on quadratic infinite programs of integral type, Appl. math. lett., 20, 6, 676-680, (2007) · Zbl 1162.49303
[36] Zimmermann, H., Fuzzy programming and linear programming with several objective functions, Fuzzy sets syst., 1, 46-51, (1978) · Zbl 0364.90065
[37] Zadeh, L.A., Toward a generalized theory of uncertainty (GTU)—an outline, Inform. sci., 172, 1-40, (2005) · Zbl 1074.94021
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