# Solution to Fuzzy Multi-Objective Assignment Problems using Diagonal Optimal Method

## Authors

• Thangaraj Beaula PG and Research Department of Mathematics, T.B.M.L. College (affiliated to Bharathidasasn University), Porayar 609307, Tamilnadu, India
• S. Saravanan Department of Mathematics, Kittappa M.H.S. School, Mayiladuthurai 609001, Tamilnadu, India

## Keywords:

Fuzzy multi-objective assignment problem, Trapezoidal fuzzy number, Ranking of fuzzy numbers, Diagonal optimal method

## Abstract

In this paper a new algorithm diagonal optimal method is proposed to obtain optimal solution to fuzzy multi-objective assignment problem with several fuzzy parameters. The method is illustrated with a numerical example.

## References

P. Biswas and S. Pramanik, Multi-objective assignment problem with fuzzy costs for the case military affairs, International Journal of Computer Applications 30(10) (2011), 7 – 12, DOI: 10.5120/3678-5179.

M. S. Chen, On a fuzzy assignment problem, Tamkang Journal of Mathematics 22 (1985), 407 – 411.

Y. Feng and L. Yang, A two-objective fuzzy k-cardinality assignment problem, Journal of Computational and Applied Mathematics 197(1) (2006), 233 – 244, DOI: 10.1016/j.cam.2005.08.026.

L. Huang and L. Zhang, Solution method for fuzzy assignment problem with restriction of qualification, in: 6th International Conference on Intelligent Systems Design and Applications, Jinan, 765 – 769 (2006), DOI: 10.1109/ISDA.2006.247.

S. Kar, K. Basu and S. Mukherjee, Solution of generalised Fuzzy assignment problem with restriction on costs under fuzzy environment, International Journal of Fuzzy Mathematics and Systems 4(2) (2004), 169 – 180.

A. Kaur and A. Kumar, A new method for solving fuzzy transportation problems using ranking function, Applied Mathematical Modelling 35(12) (2011), 5652 – 5661, DOI: 10.1016/j.apm.2011.05.012.

R. T. Marler and J. S. Arora, Survey of multi-objective optimization method for engineering, Structural and Multidisciplinary Optimization 26(6) (2004), 369 – 395, DOI: 10.1007/s00158-003-0368-6.

K. Salehi, An approach for solving multi-objective assignment problem with interval parameters, Management Science Letters 4 (2014), 2155 – 2160, DOI: 10.5267/j.msl.2014.7.031.

A. H. Taha, Operations Research, An Introduction, 5th edition, Macmillan, Basingstoke Hampshire (1992).

Y. L. P. Thorani, P. P. B. Rao and N. R. Shankar, Ordering generalized trapezoidal fuzzy numbers, International Journal Contemporary Mathematical Sciences 7(12) (2012), 555 – 573.

E. M. Vinoliah and K. Ganesan, A different approach for the solution of fuzzy multiobjective assignment problems, AIP Conference Proceedings 2112, 020118 (2019), DOI: 10.1063/1.5112303.

L. A. Zadeh, Fuzzy sets, Information and Controls 8(3) (1965), 338 – 353, DOI: 10.1016/S0019-9958(65)90241-X.

25-12-2022
CITATION

## How to Cite

Beaula, T., & Saravanan, S. (2022). Solution to Fuzzy Multi-Objective Assignment Problems using Diagonal Optimal Method. Communications in Mathematics and Applications, 13(4), 1277–1285. https://doi.org/10.26713/cma.v13i4.2185

Research Article