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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.

90C70Fuzzy programming
90C05Linear programming
90C29Multi-objective programming; goal programming
Full Text: DOI
[1] Campose, L.; Verdegay, J. L.: Linear programming problems and ranking of fuzzy numbers. Fuzzy sets and systems 32, No. 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. Multiple criteria decision making, 76-86 (1976)
[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 1, 296-297 (1971) · Zbl 0224.93016
[6] Kuhn, H. W.; Tucker, A. W.: Nonlinear programming. Proceedings of second Berkeley symposium on mathematical statistics and probability, 481-492 (1951) · 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)
[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) · 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, No. 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, No. 3, 185-194 (1991) · Zbl 0551.90062
[13] Zadeh, L. A.: Optimality and non-scalar valued performance criteria. IEEE transactions on automatic control 8, 59-60 (1963)
[14] Zhang, G. Q.: Fuzzy continuous function and its properties. Fuzzy sets and systems 43, No. 1, 159-171 (1991) · Zbl 0735.26013
[15] Zhang, G. Q.: Fuzzy limit theory of fuzzy complex numbers. Fuzzy sets and systems 46, No. 2, 227-235 (1992) · Zbl 0765.30034
[16] Zhang, G. Q.: Fuzzy number-valued measure theory. (1998) · Zbl 0920.28017