# zbMATH — the first resource for mathematics

A two-objective fuzzy $$k$$-cardinality assignment problem. (English) Zbl 1098.90064
Summary: This paper investigates a two-objective $$k$$-cardinality assignment problem. As a result, a chance-constrained goal programming model is constructed for the problem. Also, tabu search algorithm based on fuzzy simulation is designed to solve the problem. Finally, a numerical example is presented to show the application of the algorithm.

##### MSC:
 90C29 Multi-objective and goal programming 90C59 Approximation methods and heuristics in mathematical programming 90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
##### Keywords:
assignment problem; critical value; tabu search algorithm
Full Text:
##### References:
 [1] Belacela, N.; Boulasselb, M.R., Multicriteria fuzzy assignment method: a useful tool to assist medical diagnosis, Artificial intelligence in medicine, 21, 201-207, (2001) [2] Bogomolnaia, A.; Moulin, A., A new solution to the random assignment problem, J. econom. theory, 100, 295-328, (2001) · Zbl 1134.91357 [3] Bogomolnaia, A.; Moulin, H., A simple random assignment problem with a unique solution, Econom. theory, 19, 623-636, (2002) · Zbl 1022.91018 [4] Coppersmith, D.; Sorkin, G.B., Constructive bounds and exact expectation for the random assignment problem, Random structure and algorithm, 15, 2, 113-144, (1999) · Zbl 0957.90076 [5] Higgins, A.J., A dynamic tabu search for large-scale generalised assignment problems, Comput. oper. res., 28, 1039-1048, (2001) · Zbl 1017.90089 [6] Liu, B., Minimax chance constrained programming models for fuzzy decision systems, Inform. sci., 112, 25-38, (1998) · Zbl 0965.90058 [7] Liu, B., Uncertain programming, (1999), Wiley New York [8] Liu, B., Theory and practice of uncertain programming, (2002), Physica-Verlag Heidelberg · Zbl 1029.90084 [9] Liu, B.; Liu, Y.K., Expected value of fuzzy variable and fuzzy expected value models, IEEE trans. fuzzy system, 10, 4, 445-450, (2002) [10] Lin, C.J.; Wen, U.P., A labeling algorithm for the fuzzy assignment problem, Fuzzy sets and systems, 142, 373-391, (2004) · Zbl 1044.90097 [11] Mauro, D.A.; Andrea, L.; Silvano, M., Efficient algorithms and codes for $$k$$-cardinality assignment problems, Discrete appl. math., 110, 25-40, (2001) [12] Mauro, D.A.; Silvano, M., The $$k$$-cardinality assignment problem, Discrete appl. math., 76, 103-121, (1997) · Zbl 0882.90109 [13] MĂ©zard, M.; Parisi, G., On the solution of the random link matching problem, J. phys. lett., 48, 1451-1459, (1987) [14] Ridwan, M., Fuzzy preference based traffic assignment problem, Transportation res. part C, 12, 209-233, (2004) [15] Tadei, R.; Nicoletta Ricciardi, X., The dynamic multilevel assignment problem as a stochastic extremal process, European J. oper. res., 117, 264-274, (1999) · Zbl 0998.90034 [16] Volgenant, A., Solving the $$k$$-cardinality assignment problem by transformation, European J. oper. res., 157, 322-331, (2004) · Zbl 1103.90062 [17] Zadeh, L.A., Fuzzy sets, Inform. control, 8, 338-353, (1965) · Zbl 0139.24606
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.