Skip to main content
Springer Nature Link
Log in

Multi objective programming problem in the hesitant fuzzy environment

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

In this paper, we introduce a hesitant fuzzy multi-objective programming problem, in which the evaluation information provided by the decision makers is expressed in a hesitant fuzzy environment. For this purpose a new solution concept, namely hesitant fuzzy Pareto optimal solution to the problem is introduced, and two methods are proposed to obtain it. Then it is shown that the optimal solutions of these methods are the hesitant fuzzy Pareto optimal solutions. Finally, these methods are implemented on some illustrative examples and comparative analysis of our methodology is taken with other extensions of fuzzy sets.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Sakawa M (1993) Fuzzy sets and interactive multiobjective optimization. Plenum Press, New York

    Book  Google Scholar 

  2. Zimmermann HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1:45– 55

    Article  MathSciNet  Google Scholar 

  3. Sakawa M (1983) Interactive computer programs for fuzzy linear programming with multiple objectives. Int J Man-Mach Stud 18:489–503

    Article  Google Scholar 

  4. Sakawa M (1984) Interactive fuzzy decision making for multiobjective nonlinear programming problems, Interactive Decision Analysis. In: Grauer M, Wierzbicki AP (eds). Springer, Berlin, pp 105–112

  5. Lai YJ, Hwang CL (1996) Fuzzy multiple objective decision making-methods and applications. Springer, Germany

    MATH  Google Scholar 

  6. Loetamonphong J, Fang SC, Young RE (2002) Multi-objective optimization problems with fuzzy relation equation constraints. Fuzzy Sets Syst 127(2):141–164

    Article  MathSciNet  Google Scholar 

  7. Rouhbakhsh FF, Hassanpour H, Effati S (2018) Some new solution concepts in generalized fuzzy multiobjective optimization problems. Soft Computing 22(10):3261–3270

    Article  Google Scholar 

  8. Maali Y, Mahdavi-Amiri N (2014) A triangular type-2 multi-objective linear programming model and a solution strategy. Inf Sci 279:816–826

    Article  MathSciNet  Google Scholar 

  9. Rani D, Gulati TR, Garg H (2016) Multi-objective nonlinear programming problem inintuitionistic fuzzy environment: Optimistic and pessimistic view point. Expert Syst Appl 64:228–238

    Article  Google Scholar 

  10. Zhong S, Chen Y, Zhou J, Liu Y (2017) An interactive satisficing approach for multi-objective optimization with uncertain parameters. J Intell Manuf 28(3):535–547

    Article  Google Scholar 

  11. Jafarian E, Razmi J, Baki MF (2018) A flexible programming approach based on intuitionistic fuzzy optimization and geometric programming for solving multi-objective nonlinear programming problems. Expert Syst Appl 93:245–256

    Article  Google Scholar 

  12. Jiuping X (2011) A kind of fuzzy multi-objective linear programming problems based on interval valued fuzzy sets. J Syst Sci Compl 14:149–158

    MathSciNet  MATH  Google Scholar 

  13. Jana B, Roy TK (2007) Multiobjective intuitionistic fuzzy linear programming and its application in transportation model. Notes Intuit Fuzzy Sets 13(1):34–51

    Google Scholar 

  14. Bharati SK, Singh SR (2019) Solution of multiobjective linear programming problem in interval-valued intuitionistic fuzzy environment. Soft Comput 23(1):77–84

    Article  Google Scholar 

  15. Singh V, Shiv PY (2018) Modeling and optimization of multi-objective programming problems in intuitionistic fuzzy environment: optimistic, pessimistic and mixed approaches. Expert Syst Appl 102:143–157

    Article  Google Scholar 

  16. Alcantud JCR, Torra V (2018) Decomposition theorems and extension principles for hesitant fuzzy sets. Inf Fusion 41:48–56

    Article  Google Scholar 

  17. Cabrerizo FJ, Martínez M. Á, Cobo MJ, Alonso S, Herrera-Viedma E (2018) Hesitant Fuzzy Sets: A Bibliometric Study, 2018 5th International Conference on Control, Decision and Information Technologies (coDIT), Thessaloniki, 659–664

  18. Qian G, Wang H, Feng X (2013) Generalized of hesitant fuzzy sets and their application in decision support system. Knowl-Based Syst 37:357–365

    Article  Google Scholar 

  19. Ranjbar M, Effati S, Kamyad AV (2018) T-operators in hesitant fuzzy sets and their applications to fuzzy rule-based classifier. Appl Soft Comput 62:423–440

    Article  Google Scholar 

  20. Ranjbar M, Kamyad AV, Effati S (2019) Fuzzy classification as a decision making problem in hesitant environments. Int J Inf Decis Sci 11(1):22–35

    Google Scholar 

  21. Ranjbar M, Effati S (2020) Symmetric and right-hand-side hesitant fuzzy linear programming. J IEEE Trans Fuzzy Syst 28(2):215–227

    Article  Google Scholar 

  22. Rodriguez RM, Martinez L, Herrera F (2012) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 20(1):109–119

    Article  Google Scholar 

  23. Rodriguez RM, Martinez L, Torra V, Xu FS, Herrera F (2014) Hesitant fuzzy sets: State of the Art and Future Directions. Int J Intell Syst 29:495–524

    Article  Google Scholar 

  24. Rodriguez RM, Xu Z, Martinez L (2018) Hesitant fuzzy information for information fusion in decision making. Inf Fusion 42:62–63

    Article  Google Scholar 

  25. Wei GW (2012) Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowl-Based Syst 31:176–182

    Article  Google Scholar 

  26. Wu Y, Lia CC, Chen X, Dong Y (2018) Group decision making based on linguistic distributions and hesitant assessments: Maximizing the support degree with an accuracy constraint. Inf Fusion 41:151–160

    Article  Google Scholar 

  27. Xia M, Xu Z (2011) Hesitant fuzzy information aggregation in decision making. Inte J Approx Reason 52 (3):395–407

    Article  MathSciNet  Google Scholar 

  28. Xu Y, Xu A, Wang H (2016) Hesitant fuzzy linguistic linear programming technique for multidimensional analysis of preference for multi-attribute group decision making. Int J Mach Learn Cybern 7:845–855

    Article  Google Scholar 

  29. Yu D (2013) Triangular hesitant fuzzy set and its application to teaching quality evaluation. J Inf Comput Sci 10(7):1925– 1934

    Article  Google Scholar 

  30. Zhang X, Xu Z, Xing X (2016) Hesitant fuzzy programming technique for multidimensional analysis of hesitant fuzzy preferences. OR Spectrum 38(3):789–817

    Article  MathSciNet  Google Scholar 

  31. Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Manag Sci 17:141–164

    Article  MathSciNet  Google Scholar 

  32. Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision, In: The 18th IEEE international conference on fuzzy systems, Jeju Island, pp 1378–1382

  33. Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539

    MATH  Google Scholar 

  34. Werners B (1987) Interactive multiple objective programming subject to flexible constraints. Eur J Oper Res 31:342–349

    Article  MathSciNet  Google Scholar 

  35. Ehrgott M (2005) Multicriteria optimization. Springer, Berlin

  36. Zeleny M (1986) Optimal system design with multiple criteria: De Novo programming approach. Eng Costs Prod Econ 10:89–94

    Article  Google Scholar 

  37. Angelov PP (1997) Optimization in an intuitionistic fuzzy environment. Fuzzy Sets Syst 86:299–306

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematical Sciences and Statistics, University of Birjand, Birjand, Iran

    F. F. Rouhbakhsh & H. Hassanpour

  2. Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

    M. Ranjbar & S. Effati

  3. Center of Excellence of Soft Computing and Intelligent Information Processing (SCIIP), Ferdowsi University of Mashhad, Mashhad, Iran

    S. Effati

Authors
  1. F. F. Rouhbakhsh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Ranjbar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Effati
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. H. Hassanpour
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Effati.

Additional information

Publisher’s note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rouhbakhsh, F.F., Ranjbar, M., Effati, S. et al. Multi objective programming problem in the hesitant fuzzy environment. Appl Intell 50, 2991–3006 (2020). https://doi.org/10.1007/s10489-020-01682-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-020-01682-8

Keywords