Formulation of fuzzy linear programming problems as four-objective constrained optimization problems

Applied Mathematics and Computation

Volumn 139, Issue 2-3, 2003, Pages 383-399

  Zhang, Guangquan ^a   Wu, Yong Hong ^a   Remias, M ^a   Lu, Jie ^b  

^a CURTIN UNIVERSITY   (Australia)

^b UNIVERSITY OF TECHNOLOGY SYDNEY   (Australia)

Author keywords

Fuzzy number; Linear programming; Multi objective linear programming; Optimization

Indexed keywords

FUNCTIONS; FUZZY SETS; OPTIMAL SYSTEMS; OPTIMIZATION; PROBLEM SOLVING;

OPTIMAL SOLUTIONS;

LINEAR PROGRAMMING;

EID: 0037448166     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(02)00202-3     Document Type: Article

References (16)

1. Campose L., Verdegay J.L. Linear programming problems and ranking of fuzzy numbers. Fuzzy Sets and Systems. 32(1):1989;1-11.
2. Bowman V.J. On the relationship of the Tchebycheff norm and the efficient frontier of multi-criteria objectives. Thiriez H., Zionts S. Multiple Criteria Decision Making. 1976;76-86 Springer-Verlag, Berlin.
3. Furukawa N. A parametric total order on fuzzy numbers and a fuzzy shortest route problem. Optimization. 30:1994;367-377.
4. Haimes Y.Y., Hall W.A. Multiobjective in water resources systems analysis: the surrogate worth trade-off method. Water Resources Research. 10:1974;614-624.
5. Haimes Y.Y., Lasdon L., Wismer D. On a bicriteria formulation of the problems of integrated system identification and system optimization. IEEE Transactions on Systems, Man, and Cybernetics, SMC-1:1971;296-297.
6. Kuhn H.W., Tucker A.W. Nonlinear programming. Neyman J. Proceedings of Second Berkeley Symposium on Mathematical Statistics and Probability. 1951;481-492 University of California Press.
7. Luhandjura M.K. Linear programming with a possibilistic objective function. European Journal of Operational Research. 13:1987;137-145.
8. Maeda T. Multi-objective decision making and its applications to economic analysis. 1996;Makino-Syoten.
9. Maeda T. Fuzzy linear programming problems as bi-criteria optimization problems. Applied Mathematics and Computation. 120:2001;109-121.
10. Sakawa M. Fuzzy sets and interactive multiobjective optimization. 1993;Plenum Press, New York.
11. Sakawa M., Yano H. Feasibility and Pareto optimality for multi-objective programming problems with fuzzy parameters. Fuzzy Sets and Systems. 43(1):1991;1-15.
12. Tanaka H., Ichihashi H., Asai K. A formulation of fuzzy linear programming problem based on comparison of fuzzy numbers. Control and Cybernetics. 3(3):1991;185-194.
13. Zadeh L.A. Optimality and non-scalar valued performance criteria. IEEE Transactions on Automatic Control. AC-8:1963;59-60.
14. Zhang G.Q. Fuzzy continuous function and its properties. Fuzzy Sets and Systems. 43(1):1991;159-171.
15. Zhang G.Q. Fuzzy limit theory of fuzzy complex numbers. Fuzzy Sets and Systems. 46(2):1992;227-235.
16. Zhang G.Q. Fuzzy number-valued measure theory. 1998;Tsinghua University Press, Beijing.