Skip to main content

A solution algorithm for finding the best and the worst fuzzy compromise solutions of fuzzy rough linear programming problem with triangular fuzzy rough number coefficients

Abstract

An algorithm for the solution of the fuzzy rough linear programming (FRLP) problems with triangular fuzzy rough number parameters is proposed to overcome the uncertainty in decision-making problems. While the costs of the objective function and the coefficients of constraints are triangular fuzzy rough numbers, the variables are in the triangular fuzzy form. Fuzzy optimal solutions are found by solving two distinct fully fuzzy linear programming (FFLP) problems, obtained from the lower and upper approximations of the FRLP problem. These solutions are utilized to evaluate different fuzzy objective function values, and these values are compared according to their supports to specify the worst and the best fuzzy rough compromise solutions. The decision-maker (DM) can make a final decision within the bounds of these supports according to the direction of the optimization. Also, the algorithm yields approximate fuzzy rough compromise solutions in the infeasibility case of the FFLP problems. To demonstrate the efficiency of the algorithm, some numerical examples are illustrated.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Data availability statement

All data generated or analyzed during this study are cited from the published articles (Hamzehee et al 2014; Ahlatcioglu Ozkok et al 2016; Saad and Fathy 2019).

References

Download references

Acknowledgements

The author would like to thank the anonymous reviewers and editor for providing a chance to revise this paper and its quality. Also, thanks to my friend Sahika Koyun Yilmaz for helping me revise the paper during the review process.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gizem Temelcan.

Ethics declarations

Conflict of interest

The author declares that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Temelcan, G. A solution algorithm for finding the best and the worst fuzzy compromise solutions of fuzzy rough linear programming problem with triangular fuzzy rough number coefficients. Granul. Comput. (2022). https://doi.org/10.1007/s41066-022-00341-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s41066-022-00341-2

Keywords

  • Fuzzy linear programming problems
  • Fuzzy rough numbers
  • Triangular fuzzy numbers
  • Compromise solution