• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2021, Volume: 14, Issue: 6, Pages: 582-603

Original Article

q-Rung Orthopair Dual Hesitant Fuzzy Bonferron Mean Operators

Received Date:09 October 2020, Accepted Date:25 January 2021, Published Date:01 March 2021


Objectives/Methods: Taking into account the impreciseness and subjectiveness of decision makers (DMs) in complex decision-making situations, the assessment datum over alternatives given by DMs is consistently vague and uncertain. In meantime, to evaluate human’s hesitance, the q-rung orthopair dual hesitant fuzzy sets (q-RODHFSs) are defined which are more accurate for manipulation real MADM matters. To merge the datum in q-RODHFSs more precisely, in this research script, some Bonferroni mean (BM) operators in light of q-RODHFSs datum, which includes arbitrary number of being merged arguments, are developed and examined. Findings: Obviously, the novel defined operators can produce much accurate results than already existing methods. Additionally, some important measures of said BM operators are talked about and all the peculiar cases of them are studied which expresses that the BM operator is more dominant than others. Eventually, the MADM algorithm is furnished and the operators are utilized to choose the best alternative under q-rung orthopair dual hesitant fuzzy numbers (q-RODHFNs). Taking advantage of the novel operators and constructed algorithm, the developed operators are utilized in the MADM problems.

Keywords: : Bonferroni mean; Dual BM; q-rung orthopair dual hesitant fuzzy sets; q-rung orthopair dual hesitant fuzzy weighted Bonferroni mean; q-rung orthopair dual hesitant fuzzy weighted dual Bonferroni mean


  1. Atanassov KT. Intuitionistic fuzzy sets. In: Intuitionistic fuzzy sets 1999. (pp. 1-137) Heidelberg. Physica..
  2. Zadeh LA. Fuzzy sets. Information and Control. 1965;8:338–353. Available from: https://dx.doi.org/10.1016/s0019-9958(65)90241-x
  3. Torra V. Hesitant fuzzy sets. International Journal of Intelligent Systems. 2010;25(6). Available from: https://dx.doi.org/10.1002/int.20418
  4. Peng X, Yang Y. Some results for Pythagorean fuzzy sets. International Journal of Intelligent Systems. 2015;30(11):991–1029.
  5. Peng X, Yuan H, Yang Y. Pythagorean fuzzy information measures and their applications. International Journal of Intelligent Systems. 2017;32(10):991–1029.
  6. Bonferroni C. Sulle medie multiple di potenze. Bollettino dell'Unione Matematica Italiana. 1950;5(3-4):267–270.
  7. Yager RR. Generalized Orthopair Fuzzy Sets. IEEE Transactions on Fuzzy Systems. 2017;25(5):1222–1230. Available from: https://dx.doi.org/10.1109/tfuzz.2016.2604005
  8. Liu P, Wang P. Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. International Journal of Intelligent Systems. 2018;33(2):259–280.
  9. Liu P, Chen SM, Wang P. Multiple-attribute group decision-making based on q-rung orthopair fuzzy power maclaurin symmetric mean operators. IEEE Transactions on Systems, Man, and Cybernetics: Systems. 2018.
  10. Liu P, Wang P. Multiple-attribute decision-making based on Archimedean Bonferroni Operators of q-rung orthopair fuzzy numbers. IEEE Transactions on Fuzzy systems. 2018;27(5):834–848.
  11. Peng X, Dai J, Garg H. Exponential operation and aggregation operator for q-rung orthopair fuzzy set and their decision-making method with a new score function. International Journal of Intelligent Systems. 2018;33(11):2255–2282. Available from: https://dx.doi.org/10.1002/int.22028
  12. Wei G, Gao H, Wei Y. Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making. International Journal of Intelligent Systems. 2018;33(7):1426–1458.
  13. Wang J, Wei G, Lu J, Alsaadi FE, Hayat T, Wei C, et al. Some q-rung orthopair fuzzy Hamy mean operators in multiple attribute decision-making and their application to enterprise resource planning systems selection. International Journal of Intelligent Systems. 2019;34(10):2429–2458.
  14. Liu P, Ali Z, Mahmood T. A Method to Multi-Attribute Group Decision-Making Problem with Complex q-Rung Orthopair Linguistic Information Based on Heronian Mean Operators. International Journal of Computational Intelligence Systems. 2019;2019:1465–1496. Available from: https://dx.doi.org/10.2991/ijcis.d.191030.002
  15. Liu P, Liu W. Multiple-attribute group decision-making based on power Bonferroni operators of linguistic q-rung orthopair fuzzy numbers. International Journal of Intelligent Systems. 2019;34(4):652–689.
  16. Tang M, Wang J, Lu J, Wei G, Wei C, Wei Y. Dual Hesitant Pythagorean Fuzzy Heronian Mean Operators in Multiple Attribute Decision Making. Mathematics. 2019;7(4):344. Available from: https://dx.doi.org/10.3390/math7040344
  17. Zhu B, Xu Z, Xia M. Dual Hesitant Fuzzy Sets. Journal of Applied Mathematics. 2012;2012:1–13. Available from: https://dx.doi.org/10.1155/2012/879629
  18. Wang H, Zhao X, Wei G. Dual hesitant fuzzy aggregation operators in multiple attribute decision making. Journal of Intelligent & Fuzzy Systems. 2014;26(5):2281–2290.
  19. Tu NH, Wang CY, Zhou XQ, Tao SD. Dual hesitant fuzzy aggregation operators based on Bonferroni means and their applications to multiple attribute decision making. Annl. Fuzzy Math. Inform. 2017;14:265–278.


© 2021 Ayub & Malik.This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)


Subscribe now for latest articles and news.