×

Formulation of fuzzy linear programming problems as four-objective constrained optimization problems. (English) Zbl 1033.90155

Summary: This paper concerns the solution of fuzzy linear programming (FLP) problems which involve fuzzy numbers in coefficients of objective functions. Firstly, a number of concepts of optimal solutions to FLP problems are introduced and investigated. Then, a number of theorems are developed so as to convert the FLP to a multi-objective optimization problem with four-objective functions. Finally, two illustrative examples are given to demonstrate the solution procedure. It also shows that our method of solution includes an existing method as a special case.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C05 Linear programming
90C29 Multi-objective and goal programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Campose, L.; Verdegay, J. L., Linear programming problems and ranking of fuzzy numbers, Fuzzy Sets and Systems, 32, 1, 1-11 (1989) · Zbl 0674.90061
[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), Springer-Verlag: Springer-Verlag Berlin), 76-86
[3] Furukawa, N., A parametric total order on fuzzy numbers and a fuzzy shortest route problem, Optimization, 30, 367-377 (1994) · Zbl 0818.90136
[4] Haimes, Y. Y.; Hall, W. A., Multiobjective in water resources systems analysis: the surrogate worth trade-off method, Water Resources Research, 10, 614-624 (1974)
[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, 296-297 (1971) · Zbl 0224.93016
[6] Kuhn, H. W.; Tucker, A. W., Nonlinear programming, (Neyman, J., Proceedings of Second Berkeley Symposium on Mathematical Statistics and Probability (1951), University of California Press), 481-492 · Zbl 0044.05903
[7] Luhandjura, M. K., Linear programming with a possibilistic objective function, European Journal of Operational Research, 13, 137-145 (1987)
[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, 109-121 (2001) · Zbl 1032.90080
[10] Sakawa, M., Fuzzy sets and interactive multiobjective optimization (1993), Plenum Press: Plenum Press New York · Zbl 0842.90070
[11] Sakawa, M.; Yano, H., Feasibility and Pareto optimality for multi-objective programming problems with fuzzy parameters, Fuzzy Sets and Systems, 43, 1, 1-15 (1991) · Zbl 0755.90090
[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, 185-194 (1991) · Zbl 0551.90062
[13] Zadeh, L. A., Optimality and non-scalar valued performance criteria, IEEE Transactions on Automatic Control, AC-8, 59-60 (1963)
[14] Zhang, G. Q., Fuzzy continuous function and its properties, Fuzzy Sets and Systems, 43, 1, 159-171 (1991) · Zbl 0735.26013
[15] Zhang, G. Q., Fuzzy limit theory of fuzzy complex numbers, Fuzzy Sets and Systems, 46, 2, 227-235 (1992) · Zbl 0765.30034
[16] Zhang, G. Q., Fuzzy number-valued measure theory (1998), Tsinghua University Press: Tsinghua University Press Beijing
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.