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A weighted max-min model for fuzzy goal programming. (English) Zbl 1045.90091
Summary: After Narasimhan’s pioneering study of applying fuzzy set theory to goal programming in 1980, many achievements in the field have been recorded. Most of them followed the max-min approach. However, when objectives have different levels of importance, only the weighted additive model of R. N. Tiwari, S. Dharmar and J. R. Rao [ibid. 24, 27–34 (1987; Zbl 0627.90073)] seems to be applicable. However, the shortcoming of the additive model is that the summation of quasiconcave functions may not be quasiconcave. This study proposes a novel weighted max-min model for fuzzy goal programming (FGP) and for fuzzy multiple objective decision-making. The proposed model adapts well to even the most complicated membership functions. Numerical examples demonstrate that the proposed model can be effectively incorporated with other approaches to FGP and is superior to the weighted additive approach.

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
Full Text: DOI
[1] Bellman, R.; Zadeh, L.A., Decision-making in a fuzzy environment, Management sci., 17B, 141-164, (1970) · Zbl 0224.90032
[2] Dubois, D.; Fargier, H.; Prade, H., Possibility theory in constraint satisfaction problemshandling priority, preference and uncertainty, Appl. intell., 6, 287-309, (1996)
[3] Dubois, D.; Fortemps, F., Computing improved optimal solutions to max – min flexible constraint satisfaction problems, European J. oper. res., 118, 95-126, (1999) · Zbl 0945.90087
[4] Dubois, D.; Prade, H., Weighted minimum and maximum operations, Inform. sci., 39, 205-210, (1986) · Zbl 0605.03021
[5] Hannan, E.L., Linear programming with multiple fuzzy goals, Fuzzy sets and systems, 6, 235-248, (1981) · Zbl 0465.90080
[6] Inuiguchi, M.; Ichihashi, H.; Kume, Y., A solution algorithm for fuzzy linear programming with piecewise membership functions, Fuzzy sets and systems, 34, 15-31, (1990) · Zbl 0693.90064
[7] Inuiguchi, M.; Ichihashi, H.; Tanaka, H., Possibilistic linear programming with measurable multiattribute value functions, ORSA J. comput., 1, 146-158, (1989) · Zbl 0753.90072
[8] Lai, Y.J.; Hwang, C.L., Possibilistic linear programming for managing interest rate risk, Fuzzy sets and systems, 49, 121-133, (1992)
[9] R.J. Li, Multiple objective decision making in a fuzzy environment, Ph.D. Dissertation (1990), Department of Industrial Engineering, Kansas State University, Manhattan, KS.
[10] Li, H.L.; Yu, C.S., A fuzzy multiobjective program with quasiconcave membership functions and fuzzy coefficients, Fuzzy sets and systems, 109, 59-81, (2000) · Zbl 0955.90152
[11] Lin, C.C.; Chen, A.P., A generalization of Yang et al.’s method for fuzzy programming with piecewise linear membership functions, Fuzzy sets and systems, 132, 347-352, (2002) · Zbl 1099.90595
[12] Nakamura, K., Some extensions of fuzzy linear programming, Fuzzy sets and systems, 14, 211-229, (1984) · Zbl 0552.90063
[13] Narasimhan, R., Goal programming in a fuzzy environment, Decision sci., 11, 325-338, (1980)
[14] Narasimhan, R., On fuzzy goal programming—some comments, Decision sci., 12, 532-538, (1981)
[15] Sabbadin, R.; Dubois, D.; Grenier, P.; Prade, H., A fuzzy constraint satisfaction problem in the wine industry, J. intell. fuzzy systems, 6, 367-374, (1998)
[16] Tiwari, R.N.; Dharmar, S.; Rao, J.R., Priority structure in fuzzy goal programming, Fuzzy sets and systems, 19, 251-259, (1986) · Zbl 0602.90078
[17] Tiwari, R.N.; Dharmar, S.; Rao, J.R., Fuzzy goal programming—an additive model, Fuzzy sets and systems, 24, 27-34, (1987) · Zbl 0627.90073
[18] Wang, H.F.; Fu, C.C., A generalization of fuzzy programming with preemptive structure, Comput. oper. res., 24, 819-828, (1997) · Zbl 0893.90175
[19] Yang, T.; Ignizio, J.P.; Kim, H.J., Fuzzy programming with nonlinear membership functionspiecewise linear approximation, Fuzzy sets and systems, 41, 39-53, (1991) · Zbl 0743.90115
[20] Zimmermann, H.-J., Fuzzy programming and linear programming with multiple objective functions, Fuzzy sets and systems, 1, 45-55, (1978) · Zbl 0364.90065
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