On Fuzzy Linear Fractional Programming Problems via α-Cut-Based Method with Application in Transportation Sector

Abhishek Chauhan, Sumati Mahajan, Izhar Ahmad*, Suliman Al-Homidan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The article provides an (Formula presented.) -cut-based method that solves linear fractional programming problems with fuzzy variables and unrestricted parameters. The parameters and variables are considered as asymmetric triangular fuzzy numbers, which is a generalization of the symmetric case. The problem is solved by using (Formula presented.) -cut of fuzzy numbers wherein the (Formula presented.) - and r-cut are applied to the objective function and constraints, respectively. This reduces the problem into an equivalent biobjective model which leads to the upper and lower bounds of the given problem. Afterwards, the membership functions corresponding to various values of (Formula presented.) are obtained using the optimal values of the biobjective model. The proposed method is illustrated by taking an example from the literature to highlight the fallacy of an existing approach. Finally, a fuzzy linear fractional transportation problem is modelled and solved using the aforementioned technique.

Original languageEnglish
Article number419
Issue number2
StatePublished - Feb 2023

Bibliographical note

Funding Information:
The authors sincerely acknowledge the valuable suggestions and recommendations of the reviewers, which considerably improved the presentation of the paper. The first author would like to acknowledge the support provided by the Council of Scientific & Industrial Research (CSIR), India, to carry out his research work. This research was also supported by the King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, under the Small/Basic Research Grant No. SB191005.

Publisher Copyright:
© 2023 by the authors.


  • fuzzy numbers
  • linear fractional problem
  • unrestricted parameters
  • α-cut

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • Mathematics (all)
  • Physics and Astronomy (miscellaneous)


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