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Optimization of fuzzy bi-objective fractional assignment problem

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A Correction to this article was published on 03 June 2019

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Abstract

Theory and applications of fractional programming have been significantly developed in the few last decades and assignment problem is one of the fundamental combinatorial optimization problems in the branch of optimization. Generally, in real world problems, the possible values of coefficients of a linear fractional programming problem are often only imprecisely or ambiguously known to the decision maker, therefore, it would be certainly more appropriate to interpret the coefficients as fuzzy numerical data. In this article, a fuzzy bi-objective fractional assignment problem has been formulated. Here the parameters are represented by triangular fuzzy numbers and the fuzzy problem is transformed into standard crisp problem through \(\alpha \)-cut and then the compromise solution is derived by fuzzy programming.

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  • 03 June 2019

    In the original published article the “Conclusion and future scope” paragraph has been incorrectly published.

Notes

  1. Triangular Fuzzy number (TFN) A fuzzy number \({\tilde{A}}=(p,q,r)\) is said to be a triangular fuzzy number if its membership function is given by

    $$\begin{aligned}\mu _{{\tilde{A}}}=\left\{ \begin{array}{ll} \frac{x-p}{q-p} &{}\quad if\;\; p \le x \le q \\ \frac{r-x}{r-q} &{}\quad if\;\; q \le x \le r \\ 0 &{}\quad otherwise \\ \end{array} \right. \end{aligned}$$

References

  1. Akkapeddi, S.M.: Fuzzy programming with quadratic membership functions for multi-objective transportation problem. Pak. J. Stat. Oper. Res. 11(2), 231–240 (2015)

    Article  Google Scholar 

  2. Bellman, R.E., Zadeh, L.A.: Decision-making in a fuzzy environment. Manag. Sci. 17(4), B-141 (1970)

    Article  Google Scholar 

  3. Charnes, A., Cooper, W.W.: Programming with linear fractional functionals. Naval Res. Logist. Q. 9(3–4), 181–186 (1962)

    Article  Google Scholar 

  4. De, P.K., Yadav, B.: A general approach for solving assignment problems involving with fuzzy cost coefficients. Mod. Appl. Sci. 6(3), 2 (2012)

    Article  Google Scholar 

  5. Dinkelbach, W.: On nonlinear fractional programming. Manag. Sci. 13, 492–498 (1967)

    Article  Google Scholar 

  6. Gupta, R.: Decomposition method and transportation type problems with a fractional objective function. ZAMM-J. Appl. Math. Mech. (Zeitschrift fr Angewandte Mathematik und Mechanik) 57(2), 81–88 (1977)

    Article  Google Scholar 

  7. Kar, S., Basu, K., Mukherjee, S.: Solution of generalized fuzzy assignment problem with restriction on costs under fuzzy environment. Int. J. Fuzzy Math. Syst. 4, 169–180 (2014)

    Google Scholar 

  8. Kumar, A., Gupta, A., Kaur, A.: Method for solving fully fuzzy assignment problems using triangular fuzzy numbers. World Acad. Sci. Eng. Technol. Int. J. Comput. Electr. Autom. Control Inf. Eng. 3(7), 1889–1892 (2009)

    Google Scholar 

  9. Kumar, P.S., Hussain, R.J.: A method for solving balanced intuitionistic fuzzy assignment problem. Int. J. Eng. Res. Appl. 4(3), 897–903 (2014)

    Google Scholar 

  10. Lin, C.J.: A simplex-based labelling algorithm for the linear fractional assignment problem. Optimization 64(4), 929–939 (2015)

    Article  Google Scholar 

  11. Lin, C.J., Wen, U.P.: A labeling algorithm for the fuzzy assignment problem. Fuzzy Sets Syst. 142(3), 373–391 (2004)

    Article  Google Scholar 

  12. Pandian, P., Kavitha, K.: A new method for solving fuzzy assignment problems. Ann. Pure Appl. Math. 1, 69–83 (2012)

    Google Scholar 

  13. Sadia, S., Gupta, N., Ali, Q.M.: Multiobjective capacitated fractional transportation problem with mixed constraints. Math. Sci. Lett. 5(3), 235–242 (2016)

    Article  Google Scholar 

  14. Sakawa, M., Nishizaki, I., Uemura, Y.: Interactive fuzzy programming for two-level linear and linear fractional production and assignment problems: a case study. Eur. J. Oper. Res. 135(1), 142–157 (2001)

    Article  Google Scholar 

  15. Saruwatari, Y., Shigeno, M., Matsui, T.: An algorithm for fractional assignment problems. Discrete Appl. Math. 56(2), 333–343 (1995)

    Google Scholar 

  16. Swarup, K.: Transportation technique in linear fractional functional programming. J. R. Naval Sci. Serv. 21(5), 256–260 (1966)

    Google Scholar 

Download references

Acknowledgements

The author express their sincere thanks to editor and referees for their valuable suggestions and comments, which improved the quality of the paper.

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  1. Faculty of Management Sciences, Amity University, Noida, India

    Neha Gupta

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  1. Neha Gupta
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Gupta, N. Optimization of fuzzy bi-objective fractional assignment problem. OPSEARCH 56, 1091–1102 (2019). https://doi.org/10.1007/s12597-019-00367-2

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