Document Type : Research Paper


1 Department of Electrical Engineering, Shohadaye Hoveizeh Campus of Technology, Shahid Chamran University of Ahvaz, Dasht-e Azadegan, Khuzestan, Iran.

2 Department of Mathematics, Behbahan Khatam Alanbia University of Technology, Behbahan, Khuzestan, Iran.


For the three last decades, the multi-objective fractional programming problem has attracted the attention of many researchers due to various applications in production planning, financial field, and inventory management, and so on. The main aim of this study is to introduce a new application of hesitant fuzzy sets in real-life modeling. We intend to model multi-objective linear fractional programming problems under a hesitant fuzzy environment and present a procedure to solve them. the increasing applications of multi-objective linear fractional programming problems and the lack of research papers in this field under a hesitant fuzzy environment are the main motivations of this study. In a hesitant fuzzy set, the membership degree of an element belongs to the set can be represented by several possible values in [0,1]. These values can be chosen by different experts that cannot reach a single opinion in determining a membership degree. so, in our model several evaluations for each of goals established by decision makers based on their attitudes. The generalization of the fuzzy decision-making principle and some new concepts provide an effective solution procedure for the problem. Finally, a practical example is extended to illustrate the applicability of the proposed method.


Main Subjects

  1. Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management science, 17(4), B-141.
  2. Charnes, A., & Cooper, W. W. (1962). Programming with linear fractional functionals. Naval Research logistics quarterly, 9(3‐4), 181-186.
  3. Choo, E. U., & Atkins, D. R. (1980). An interactive algorithm for multicriteria programming. Computers and operations research, 7(1-2), 81-87.
  4. Craven, B. D. (1988). Fractional programming, (Vol. 4). Berlin, Heldermann.
  5. Darehmiraki, M. (2019). A novel parametric ranking method for intuitionistic fuzzy numbers. Iranian journal of fuzzy systems, 16(1), 129-143.
  6. Das, S. K., Edalatpanah, S. A., & Mandal, T. (2018). A proposed model for solving fuzzy linear fractional programming problem: Numerical Point of View. Journal of computational science, 25, 367-375.‏
  7. Das, S. K., Mandal, T., & Edalatpanah, S. A. (2017). A new approach for solving fully fuzzy linear fractional programming problems using the multi-objective linear programming. RAIRO-operations research, 51(1), 285-297.‏
  8. Das, S. K., & Mandal, T. (2017). A new model for solving fuzzy linear fractional programming problem with ranking function. Journal of applied research on industrial engineering, 4(2), 89-96.‏
  9. Das, S. K., Edalatpanah, S. A., & Mandal, T. (2019). A new method for solving linear fractional programming problem with absolute value functions. International journal of operational research, 36(4), 455-466.‏
  10. Dong, J., & Wan, S. (2019). A new method for solving fuzzy multi-objective linear programming problems. Iranian journal of fuzzy systems, 16(3), 145-159.‏
  11. Gupta, P., & Bhatia, D. (2001). Sensitivity analysis in fuzzy multiobjective linear fractional programming problem. Fuzzy sets syst, 122(2), 229-236.
  12. Guzel, N., & Sivri, M. (2005). Taylor series solution of multi-objective linear fractional programming problem. Trakya university journal science, 6(2), 80-87.
  13. Hannan, E. L. (1981). Linear programming with multiple fuzzy goals. Fuzzy sets and systems, 6(3), 235-248.
  14. Kornbluth, J. S., & Steuer, R. E. (1981). Goal programming with linear fractional criteria. European journal of operational research, 8(1), 58-65.
  15. Kornbluth, J. S., & Steuer, R. E. (1981). Multiple objective linear fractional programming. Management science, 27(9), 1024-1039.
  16. Lotfi, F. H., Noora, A. A., Jahanshahloo, G. R., Khodabakhshi, M., & Payan, A. (2010). A linear programming approach to test efficiency in multi-objective linear fractional programming problems. Applied mathematical modelling, 34(12), 4179-4183.
  17. Luhandjula, M. K. (1984). Fuzzy approaches for multiple objective linear fractional optimization. Fuzzy sets and systems, 13(1), 11-23.
  18. Pal, B. B., Moitra, B. N., & Maulik, U. (2003). A goal programming procedure for fuzzy multi-objective linear fractional programming problem. Fuzzy sets and systems, 139(2), 395-405.
  19. Pramy, F. A. (2018). An approach for solving fuzzy multi-objective linear fractional programming problems. International journal of mathematical, engineering and management sciences, 3(3), 280-293.
  20. Ranjbar, M., & Effati, S. (2019). Symmetric and right-hand-side hesitant fuzzy linear programming. IEEE transactions on fuzzy systems, 28(2), 215-227.
  21. Sakawa, M., & Yano, H. (1988). An interactive fuzzy satisficing method for multi-objective linear fractional programming problems. Fuzzy sets and systems, 28(2), 129-144.
  22. Stanojević, B., & Stanojević, M. (2013). On the efficiency test in multi-objective linear fractional programming problems by Lotfi et al. 2010. Applied mathematical modelling, 37(10-11), 7086-7093.
  23. Torra, V., & Narukawa, Y. (2009, August). On hesitant fuzzy sets and decision. 2009 IEEE international conference on fuzzy systems (pp. 1378-1382). IEEE.
  24. Torra, V. (2010). Hesitant fuzzy sets. International journal of intelligent systems, 25(6), 529-539.
  25. Veeramani, C., & Sumathi, M. (2016). A new method for solving fuzzy linear fractional programming problems. Journal of intelligent & fuzzy systems, 31(3), 1831-1843.‏
  26. Wan, S. P., & Dong, J. Y. (2014). Possibility linear programming with trapezoidal fuzzy numbers. Applied mathematical modelling, 38(5-6), 1660-1672.‏
  27. Wan, S. P., & Li, D. F. (2013). Atanassov's intuitionistic fuzzy programming method for heterogeneous multiattribute group decision making with Atanassov's intuitionistic fuzzy truth degrees. IEEE transactions on fuzzy systems, 22(2), 300-312.‏
  28. Wan, S. P., & Li, D. F. (2015). Fuzzy mathematical programming approach to heterogeneous multiattribute decision-making with interval-valued intuitionistic fuzzy truth degrees. Information sciences, 325, 484-503.‏
  29. Xia, M., Xu, Z., & Chen, N. (2013). Some hesitant fuzzy aggregation operators with their application in group decision making. Group decision and negotiation, 22(2), 259-279.
  30. Xu, G. L., Wan, S. P., & Dong, J. Y. (2016). A hesitant fuzzy programming method for hybrid MADM with incomplete attribute weight information. Informatica, 27(4), 863-892.‏
  31. Zhang, R., Xu, Z., & Gou, X. (2021). An integrated method for multi-criteria decision-making based on the best-worst method and Dempster-Shafer evidence theory under double hierarchy hesitant fuzzy linguistic environment. Applied intelligence, 51(2), 713-735.