

Fuzzy Assignment Problem: A New Solution Approach
Abstract
In this paper we propose a new method to find the
fuzzy optimal solution of assignment problems with fuzzy parameters.
We develop fuzzy version of Hungarian algorithm for the solution of
fuzzy assignment problems without converting them to classical
assignment problems. The proposed method is easy to understand and
to apply for finding solution of fuzzy assignment problems occurring
in real life situations. To illustrate the proposed method an example is
provided and the obtained results are discussed.
Keywords
References
R. Amphora, H.L. Bhatia, M.C. Puri, Bi-criteria assignment problem,
Opsearch, 19 (1982) 84–96.
Y. Anzai, On integer fractional programming, J. Operation. Res. Soc.
Japan. 17 (1974) 49–66.
M.L. Balinski, R.E. Gomory, A primal method for the assignment and
transportation problems, Management Sci., 10 (1964) 578–593.
R. E. Bellman, L.A. Zadeh, Decision making in a fuzzy environment,
Management Sci., 17 (4) (1970) 141–164.
S. Chanas, D. Kuchta, A concept of the optimal solution of the
transportation problem with fuzzy cost, Fuzzy Sets and Systems, 82
(1996) 299–305.
S. Chanas, W. Kolodziejczyk, A. Machai, A Fuzzy approach to the
transportation problem , Fuzzy Sets and Systems, 13 (1984) 211-221.
S. Chanas, D. Kuchta, Fuzzy integer transportation problem, Fuzzy Sets
and Systems, 98 (1998) 291-298.
M.S .Chen, On a fuzzy assignment problem, Tamkang Journal of
Mathematics, 22 (1985) 407-411.
Chi-Jen Lin , Ue-pyng Wen, A labeling algorithm for the fuzzy
assignment problem, Fuzzy Sets and Systems, 142 (2004) 373-39.
D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and
Applications, Academic Press, New York, 1980.
D. Dubois, P. Fortemps, Computing improved optimal solutions to
max-min flexible constraint satisfaction problems, European J.
Operations Research, 118 (1999) 95-126.
K. Ganesan and P Veeramani, On Arithmetic Operations of Interval
Numbers, International Journal of Uncertainty, Fuzziness and Knowledge
- Based Systems, 13 (6) (2005) 619 - 631.
K. Ganesan and P Veeramani, Fuzzy Linear Programs with Trapezoidal
Fuzzy Numbers, Annals of Operations Research, 143 (2006) 305 – 315.
B.E. Gillett, Introduction to Operations Research-A Computer - Oriented
Algorithm Approach, McGraw-Hill, New York, 1976.
H. Haken, M. Schanz, J. Starke, Treatment of combinatorial optimization
problems using selection equations with cost terms. Part I.
Two-dimensional assignment problems, Physica D, 134(1999) 227-241.
Huang Long-sheng and Zhang Li-pu, Solution method for Fuzzy
Assignment problem with Restriction of Qualification, Proceedings of the
Sixth International Conference on Intelligent Systems Design and
Applications(ISDA’06 ), 2006.
E. Kaucher, Interval analysis in extended interval space IR, Comput.
Suppl., 2 (1980) 33–49.
H.W. Kuhn, The Hungarian method for the assignment problem, Naval
Res. Logistic. Quart, 2 (1956) 253–25.
L. Li, K. K. Lai, A fuzzy approach to the multi objective transportation
problem, Comput. Oper. Res., 27 (2000) 43–57.
R. Malhotra, H.L. Bhatia, M.C. Puri, Bi-criteria assignment problem,
Opsearch, 19 (1982) 84–96.
T. Nirmala, D. Datta, H. S. Kushwaha and K. Ganesan, Inverse Interval
Matrix: A New Approach, Applied Mathematical Sciences, 5 (13) (2011)
– 624.
G. Ramesh and K. Ganesan, Interval Linear Programming with
generalized interval arithmetic, International Journal of Scientific &
Engineering Research Volume 2, Issue 11, November-2011
M. Sakawa, I. Nishizaki, Y. Uemura, Interactive fuzzy programming for
two level linear and linear fractional production and assignment
problems: a case study , European J.Oper.Res, 135 (2001) 142-157.
Sathi Mukherjee and Kajla Basu, A More Realistic Assignment Problem
with Fuzzy Costs and Fuzzy Restrictions, Advances in Fuzzy
Mathematics, 5 (3) (2010) 395-404.
M. L Oh L Eigeartaigh, A fuzzy transportation algorithm, Fuzzy Sets and
Systems, 8 (1982) 235-243.
X. Wang, Fuzzy optimal assignment problem, Fuzzy Math. 3 (1987)
–108.
B. Werner’s, Interactive multiple objective programming subject to
flexible constraints, European J. Oper. Res., 31 (1987) 342–349.
R. R. Yager, A procedure for ordering fuzzy subsets of the unit interval,
Information Sciences, 24 (1981) 143-161.
Zadeh. L. A, Fuzzy sets, Information and control, 8 (1965) 338-353.
H. J. Zimmermann, Fuzzy set theory and its applications, Fourth Edition,
Kluwer Academic publishers, (1998)
Refbacks
- There are currently no refbacks.