Abstract
In this paper we propose an interactive fuzzy programming method for obtaining a satisfactory solution to a “bi-level quadratic fractional programming problem” with two decision makers (DMs) interacting with their optimal solutions. After determining the fuzzy goals of the DMs at both levels, a satisfactory solution is efficiently derived by updating the satisfactory level of the DM at the upper level with consideration of overall satisfactory balance between both levels. Optimal solutions to the formulated programming problems are obtained by combined use of some of the proper methods. Theoretical results are illustrated with the help of a numerical example.
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References
Baker, J.E. (1985). “Adaptive Selection Method for Genetic Algorithm and their Applications.” Proceedings of the International Conference on Genetic Algorithm and their Applications, 101–111.
Bellman, R.E. and L.A. Zadeh. (1970). “Decision Making in Fuzzy Environment.” Management Sci 17, 141–164.
Bialas, W.F. and M.H. Karwan. (1984). “Two Level Linear Programming.” Management Sci 30, 1004–1020.
Charnes, A. and W.W. Cooper. (1962). “Programming with Linear Fractional Functions.” Naval Res.. Logist. Quart 9, 181–186.
Joines, J.A. and C.Houck. (1994). On the Use of Non-Stationary Penalty Function to Solve Nonlinear Constrained Optimization Problems with GAs, in: Z. Michalewicz (Ed), Proceeding of first IEEE International Conference on Evolutionary Computation, Vol.2, IEEE Service Center, Piscataway, NJ, 579–584.
Kornbluth, J.S.H. and R.E.Steur. (1981). “Goal Programming with Linear Fractional Criteria.” European J, Oper, Res 8, 58–65.
Lai, Y.J. (1996). “Hierarchical Optimization: A Satisfactory Solution.” Fuzzy Sets and Systems 77, 321–335.
Nykowski, I. and Z. Zdkiewski. (1985). “A Compromise Procedure for the Multiple Objective Linear Fractional Programming.” European Journal of Operational Research, 1991–97.
Sakawa, M. and T. Yumine. (1983). “Interactive Fuzzy Decision Making for Multi Objective Linear Fractional Programming Problems.” Large Scale Systems 5, 105–113.
Sakawa, M., I. Nishizaki, and Y. Uemura. (1998). “Interactive Fuzzy Programming for Multi-Level Linear Programming Problem.” Computer, Math. Appl. 36, 71–86.
Sakawa, M. and I. Nishizaki. (2001). “Interactive Fuzzy Programming for Two-Level Linear Fractional Programming Problems.” Fuzzy Sets and Systems 119, 31–40.
Sakawa, M. (1993). “Fuzzy Sets and Interactive Multi Objective Optimization.” Plenum Press, New York, [13].
Schaible, S. and T.Ibaraki. (1983). “Fractional Programming.” European Journal of Operational Research, 12, 325–338.
Shih, Hsu-Shih., Young-Jou Lai and E. Stanley. (1996). “Fuzzy Approach for Multi-Level Programming Problem.” Computers O.R, 23 (1) 73–91.
Shimuzu, K., Y.Ishizuku and J.F.Bard. (1997). “Nondifferetiable and Two Level Mathematical Programming.” Kluwer Academic Publishers. Boston.
Sinha, S. and M.P.Biswal. (2000). “Fuzzy Programming Approach to Bi-Level Linear Programming Problems.” The Journal of Fuzzy Mathematics vol 8, no. 2, Los Angels.
Zimmermann, H.J. (1978). “Fuzzy programming and Linear Programming with Several Objective Functions.” Fuzzy Sets and Systems 1, 45–55.
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Mishra, S., Ghosh, A. Interactive fuzzy programming approach to Bi-level quadratic fractional programming problems. Ann Oper Res 143, 251–263 (2006). https://doi.org/10.1007/s10479-006-7386-x
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DOI: https://doi.org/10.1007/s10479-006-7386-x