Research Article
Article:Computing Improved Fuzzy Optimal Hungarian Assignment Problems with Fuzzy Costs Under Robust Ranking Techniques
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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| Volume 6 - Issue 4 |
| Published: September 2010 |
| Authors: R.Nagarajan, A.Solairaju |
10.5120/1070-1398
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R.Nagarajan, A.Solairaju . Article:Computing Improved Fuzzy Optimal Hungarian Assignment Problems with Fuzzy Costs Under Robust Ranking Techniques. International Journal of Computer Applications. 6, 4 (September 2010), 6-13. DOI=10.5120/1070-1398
@article{ 10.5120/1070-1398,
author = { R.Nagarajan,A.Solairaju },
title = { Article:Computing Improved Fuzzy Optimal Hungarian Assignment Problems with Fuzzy Costs Under Robust Ranking Techniques },
journal = { International Journal of Computer Applications },
year = { 2010 },
volume = { 6 },
number = { 4 },
pages = { 6-13 },
doi = { 10.5120/1070-1398 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2010
%A R.Nagarajan
%A A.Solairaju
%T Article:Computing Improved Fuzzy Optimal Hungarian Assignment Problems with Fuzzy Costs Under Robust Ranking Techniques%T
%J International Journal of Computer Applications
%V 6
%N 4
%P 6-13
%R 10.5120/1070-1398
%I Foundation of Computer Science (FCS), NY, USA
Abstract
Assignment problem (AP) is a well known topic and is used very often in solving problems of engineering and management science. In this problem aij denotes the cost for assigning the jth job to the ith person. The cost is usually deterministic in nature. In this paper ãij has been considered to be trapezoidal and triangular numbers denoted by ãij which are more realistic and general in nature. Robust’s ranking method [10] has been used for ranking the fuzzy numbers. The fuzzy assignment problem has been transformed into crisp assignment problem in the linear programming problem form and solved by using Hungarian method; Numerical examples show that the fuzzy ranking method offers an effective tool for handling the fuzzy assignment problem.
References
- C.B Chen and C.M.Klein, “ A Simple approach to ranking a group of aggregated fuzzy utilities,” IEEE Trans.Syst., Man, Cybern.B, vol.SMC-27, PP. 26-35, 1997.
- Chi-Jen Lin, Ue-Pyng Wen, A labeling algorithm for the fuzzy assignment Problem, Fuzzy Sets and Systems 142 (2004) 373-391.
- D.Dubois, P. Fortemps, Computing improved optimal solutions to max-min flexible constraint satisfactions
- F.Choobinesh and H.Li, “ An index for ordering fuzzy numbers,” Fuzzy sets ans Systems, vol 54, pp.287-294, 1993.
- M.OL h EL igearaigh, A fuzzy transportation algorithm,Fuzzy sets and Systems 8 (1982) 235-243.
- 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.Oer.Res.135(2001) 142-157.
- M.S.Chen, On a fuzzy assignment problem, Tamkang J. , Fuzzy Sets and Systems 98(1998) 291-29822 (1985) 407-411.
- M.Tada,H.Ishii, An integer fuzzy transportation problem, Comput.Math.Appl.31(1996) 71-87.
- P.Fortemps and M.Roubens, “ Ranking and defuzzification methods based area compensation” Fuzzy Sets and Systems, vol.82, pp 319-330, 1996.
- R.R.Yager, “ A procedure for ordering fuzzy subsets of the unit interval, Information Sciences, 24,(1981), 143-161.
- S.Chanas,D.Kuchta, A concept of the optimal solution of the transportation problem with fuzzy cost coefficients, Fuzzy Sets and Systems 82(1996) 299-305.
- S.Chanas, D.Kuchta, Fuzzy integer transportation problem problems, European J.Operations Research, 118(1999) 95-126.
- S.Chanas, W.Kolodziejczyk, A. Machaj, A fuzzy approach to the transportation problem, Fuzzy Sets and Systems 13 (1984) 211-221.
- S.H.Chen, “ Ranking fuzzy numbers with maximizing set and minimizing set”, Fuzzy Sets and Systems, 17(1985) 113-129.
- X.Wang, Fuzzy optimal assignment problem, Fuzzy Math.3(1987) 101-108.
- Zadeh L.A, Fuzzy sets, Information and control 8 (1965) 338-353.
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