A two-phase approach for multi-objective programming problems with fuzzy coefficients. (English) Zbl 1121.90134

Summary: A two-phase procedure is introduced to solve multi-objective fuzzy linear programming problems. The procedure provides a practical solution approach, which is an integration of fuzzy parametric programming (FPP) and fuzzy linear programming (FLP), for solving real life multiple objective programming problems with all fuzzy coefficients. The interactive concept of the procedure is performed to reach simultaneous optimal solutions for all objective functions for different grades of precision according to the preferences of the decision-maker (DM). The procedure can be also performed to obtain lexicographic optimal and/or additive solutions if it is needed. In the first phase of the procedure, a family of vector optimization models is constructed by using FPP. Then in the second phase, each model is solved by FLP. The solutions are optimal and each one is an alternative decision plan for the DM.


90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C29 Multi-objective and goal programming
Full Text: DOI


[1] Arıkan, F.; Güngör, Z., An application of fuzzy goal programming to a multiobjective project network problem, Fuzzy Sets and Systems, 119, 49-58 (2001)
[2] Arıkan, F.; Güngör, Z., A parametric model for cell formation and exceptional elements’ problems with fuzzy parameters, Journal of Intelligent Manufacturing, 16, 103-114 (2005)
[3] Bellman, R. E.; Zadeh, L. A., Decision making in a fuzzy environment, Management Science, 17, 2, 141-164 (1970) · Zbl 0224.90032
[4] Carlsson, C.; Korhonen, P., A Parametric approach to fuzzy linear programming, Fuzzy Sets and Systems, 20, 17-30 (1986) · Zbl 0603.90093
[5] Fabian, C.; Ciobanu, G.; Stoica, M., Interactive polyoptimization for fuzzy mathematical programming, (Lai, Y. J.; Hwang, C. L., Fuzzy Multiple Objective Decision Making-methods and Applications (1996), Springer-Verlag: Springer-Verlag Germany), 232-236 · Zbl 0637.90059
[6] Lai, Y. J.; Hwang, C. L., A new approach to some possibilistic linear programming problems, Fuzzy Sets and Systems, 49, 121-133 (1992)
[7] Lai, Y. J.; Hwang, C. L., Fuzzy Multiple Objective Decision Making-methods and Applications (1996), Springer-Verlag: Springer-Verlag Germany
[8] Leung, Y., Compromise programming under fuzziness, Control and Cybernetics, 14, 325-328 (1984) · Zbl 0551.90082
[9] Leung, Y., Hierarchical programming with fuzzy objective and constraints, (Lai, Y. J.; Hwang, C. L., Fuzzy Multiple Objective Decision Making-methods and Applications (1996), Springer-Verlag: Springer-Verlag Germany), 232-236
[10] Li, R. J.; Lee, E. S., Multi-criteria de novo programming with fuzzy parameters, Computers and Mathematics with Applications, 19, 13-20 (1990) · Zbl 0697.90075
[11] Narasimhan, D., Goal programming in a fuzzy environment, Decision Science, 11, 325-336 (1980)
[13] Parra, M. A.; Terol, A. B.; Uria, R. M.V., Solving the multiobjective possibilistic linear programming problem, European Journal of Operational Research, 117, 175-182 (1999) · Zbl 0998.90090
[14] Parra, M. A.; Terol, A. B.; Gladish, B. P.; Uria, M. V.R., Solving a multiobjective possibilistic problem through compromise programming, European Journal of Operational Research, 164, 748-759 (2005) · Zbl 1057.90056
[15] Rommelfanger, H., Interactive decision making in fuzzy linear optimization problems, European Journal of Operational Research, 41, 210-217 (1989) · Zbl 0672.90103
[16] Sakawa, M.; Yano, H., An interactive fuzzy satisfying method for multiobjective linear programming problems with fuzzy parameters, Fuzzy Sets and Systems, 35, 125-142 (1990) · Zbl 0715.90098
[17] Sasaki, M. Y.; Gen, M.; Ida, K., An efficient algorithm for solving fuzzy multiobjective 0-1 linear programming problem, Computers and Industrial Engineering, 21, 647-651 (1991)
[18] Slowinski, R., A multicriteria fuzzy linear programming methods for water supply system development planning, Fuzzy Sets and Systems, 19, 217-237 (1986) · Zbl 0626.90085
[19] Tabucanon, M. T., Multiple Criteria Decision Making in Industry (1988), Elsevier Science Publishers: Elsevier Science Publishers Amsterdam
[20] Tanaka, H.; Asai, K., Fuzzy linear programming problems with fuzzy numbers, Fuzzy Sets and Systems, 13, 1-10 (1984) · Zbl 0546.90062
[21] Werners, B., An interactive fuzzy programming system, Fuzzy Sets and Systems, 23, 131-147 (1987) · Zbl 0634.90076
[22] Wierzchon, S. T., Linear programming with fuzzy sets: a general approach, Mathematical Modelling, 9, 447-459 (1987) · Zbl 0629.90059
[23] Zadeh, L. A., Fuzzy sets, Information and Control, 8, 338-353 (1965) · Zbl 0139.24606
[24] Zadeh, L. A., Toward a generalized theory of uncertainty (GTU) - an outline, Information Sciences, 172, 1-40 (2005) · Zbl 1074.94021
[25] Zimmermann, H. J., Description and optimization of fuzzy systems, International Journal of General Systems, 2, 4, 209-215 (1976) · Zbl 0338.90055
[26] Zimmermann, H. J., Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1, 1, 45-55 (1978) · Zbl 0364.90065
[27] Zimmermann, H. J., Fuzzy Set Theory and its Applications (1987), Kluwer Academic Publishers: Kluwer Academic Publishers Boston, USA
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