Duality in fuzzy number linear programming by use of a certain linear ranking function. (English) Zbl 1102.90080

Summary: We explore some duality properties in fuzzy number linear programming problems. By use of a linear ranking function we introduce the dual of fuzzy number linear programming primal problems. We then present several duality results.


90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C46 Optimality conditions and duality in mathematical programming
03E72 Theory of fuzzy sets, etc.
90C05 Linear programming
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[1] Bazaraa, M. S.; Jarvis, J. J.; Sherali, H. D., Linear Programming and Network Flows (1990), John Wiley: John Wiley New York · Zbl 0722.90042
[2] Bellman, R. E.; Zadeh, L. A., Decision making in a fuzzy environment, Manag. Sci., 17, 141-164 (1970) · Zbl 0224.90032
[3] Bezdek, J. C., Fuzzy models—What are they, and Why?, IEEE Trans. Fuzzy Sys., 1, 1, 1-9 (1993)
[4] Dubois, D.; Prade, H., Fuzzy Sets and Systems, Theory and Applications (1980), Academic Press: Academic Press New York · Zbl 0444.94049
[5] Fang, S. C.; Hu, C. F., Linear programming with fuzzy coefficients in constraints, Comput. Math. Appl., 37, 63-76 (1999) · Zbl 0931.90069
[6] Fortemps, P.; Roubens, M., Ranking and defuzzification methods based on area compensation, Fuzzy Sets Sys., 82, 319-330 (1996) · Zbl 0886.94025
[7] Fuller, R.; Zimmermann, H. J., Fuzzy reasoning for solving fuzzy mathematical programming problems, Fuzzy Sets Sys., 60, 121-133 (1993) · Zbl 0795.90086
[8] Garcia-Aguado, C.; Verdegay, J. L., On the sensitivity of membership functions for fuzzy linear programming problems, Fuzzy Sets Sys., 56, 47-49 (1993) · Zbl 0804.90137
[9] Gasimov, R. N.; Yenilmez, K., Solving fuzzy linear programming problems with linear membership function, Turk. J. Math., 26, 375-396 (2002) · Zbl 1022.90044
[10] Lai, Y. J.; Hwang, C. L., Fuzzy Mathematical Programming Methods and Applications (1992), Springer: Springer Berlin
[11] Maleki, H. R., Ranking functions and their applications to fuzzy linear programming, Far East J. Math. Sci. (FJMS), 4, 283-301 (2002) · Zbl 1006.90093
[12] Maleki, H. R.; Tata, M.; Mashinchi, M., Linear programming with fuzzy variables, Fuzzy Sets Sys., 109, 21-33 (2000) · Zbl 0956.90068
[13] Mishmast Nehi, H.; Maleki, H. R.; Mashinchi, M., Solving fuzzy number linear programming problem by Lexicographic ranking function, Italian J. Pure Appl. Math., 15, 9-20 (2004) · Zbl 1178.90361
[14] Negoita, C. V., Fuzziness in Management (1970), OPSA/TIMS: OPSA/TIMS Miami · Zbl 0345.68048
[15] Shoacheng, T., Interval number and fuzzy number linear programming, Fuzzy Sets Sys., 66, 301-306 (1994)
[16] Tanaka, H.; Asai, K., Fuzzy linear programming problems with fuzzy numbers, Fuzzy Sets Sys., 13, 1-10 (1984) · Zbl 0546.90062
[17] Tanaka, H.; Ichihashi, H., A formulation of fuzzy linear programming problem based on comparison of fuzzy numbers, Control Cyber., 13, 185-194 (1984) · Zbl 0551.90062
[18] Tanaka, H.; Okuda, T.; Asai, K., On fuzzy mathematical programming, J. Cyber., 3, 37-46 (1984) · Zbl 0297.90098
[19] Zimmermann, H. J., Fuzzy mathematical programming, Comput. Oper. Res., 10, 4, 291-298 (1993)
[20] Zimmermann, H. J., Fuzzy Set Theory and its Applications (1996), Kluwer Academic: Kluwer Academic Norwell, MA · Zbl 0845.04006
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