Skip to main content
SpringerLink
Log in

Multi-attribute group decision-making based on Bonferroni mean operators for picture hesitant fuzzy numbers

  • Fuzzy systems and their mathematics
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

The picture hesitant fuzzy sets are an important way to express uncertain information, and they are superior to the intuitionistic fuzzy sets and the hesitant fuzzy sets. Their eminent characteristic is that the sum of the supremum of the membership degree, the abstinence degree, and the non-membership is equal to or less than 1, so the space of uncertain information they can describe is broader. Under these environments, we propose the picture hesitant fuzzy Bonferroni mean operator, picture hesitant fuzzy weighted Bonferroni mean operator, picture hesitant fuzzy geometric Bonferroni mean operator, and picture hesitant fuzzy weighted geometric Bonferroni mean operator to deal with the decision information, and some important properties of these are proved. Further, based on these operators, we presented a new method to deal with the multi-attribute group decision-making problems. Finally, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing these with other existing methods.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Abualigah L, Diabat A (2021) Advances in sine cosine algorithm: a comprehensive survey. Artif Intell Rev 2(1):1–42

    Google Scholar 

  • Abualigah L, Dulaimi AJ (2021) A novel feature selection method for data mining tasks using hybrid sine cosine algorithm and genetic algorithm. Clust Comput, 0(0), 1–16

  • Abualigah L, Yousri D, Abd Elaziz M, Ewees AA, Al-qaness MA, Gandomi AH (2021a) Aquila Optimizer: A novel meta-heuristic optimization Algorithm. Comput Ind Eng 157:107250

    Article  Google Scholar 

  • Abualigah L, Diabat A, Mirjalili S, Abd Elaziz M, Gandomi AH (2021b) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376:113609

    Article  MathSciNet  MATH  Google Scholar 

  • Al-Quran A, Alkhazaleh S (2018) Relations between the complex neutrosophic sets with their applications in decision making. Axioms 7 (3):64–81

    Article  Google Scholar 

  • Ali Z, Mahmood T (2020) Maclaurin symmetric mean operators and their applications in the environment of complex q-rung orthopair fuzzy sets. Comput Appl Math 39:1–27

    Article  MathSciNet  MATH  Google Scholar 

  • Ali Z, Mahmood T, Yang MS (2020a) TOPSIS method based on complex spherical fuzzy sets with Bonferroni mean operators. Mathematics 8(10):1739–1751

    Article  Google Scholar 

  • Ali Z, Mahmood T, Yang MS (2020b) Complex T-spherical fuzzy aggregation operators with application to multi-attribute decision making. Symmetry 12(8):1311–1338

    Article  Google Scholar 

  • Ali M, Smarandache F (2017) Complex neutrosophic set. Neural Comput Appl 28(7):1817–1834

    Article  Google Scholar 

  • Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  MATH  Google Scholar 

  • Atanassov KT (1994) New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets Syst 61(2):137–142

    Article  MathSciNet  MATH  Google Scholar 

  • Atanassov K, Szmidt E, Kacprzyk J (2017) Multiplicative type of operations over intuitionistic fuzzy pairs. In: International conference on flexible query answering systems (201–208). Springer, Cham

  • Beg I, Rashid T (2014) Group decision making using intuitionistic hesitant fuzzy sets. Int J Fuzzy Logic Intell Syst 14(3):181–187

    Article  Google Scholar 

  • Bi L, Zeng Z, Hu B, Dai S (2019) Two classes of entropy measures for complex fuzzy sets. Mathematics 7(1):96–114

    Article  Google Scholar 

  • Bonferroni C (1950) Sulle medie multiple di potenze. Bollettino Dell’unione Matematica Italiana 5(3–4):267–270

    MathSciNet  MATH  Google Scholar 

  • Chen N, Xu Z, Xia M (2013) Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model 37(4):2197–2211

    Article  MathSciNet  MATH  Google Scholar 

  • Cuong BC (2013a) Picture fuzzy sets - first results. Part 1, Seminar Neuro-Fuzzy Systems with Applications. Preprint 03/2013 Institute of Mathematics Hanoi

  • Cuong BC (2013b) Picture fuzzy sets - first results. Part 2, Seminar Neuro-Fuzzy Systems with Applications. Preprint 04/2013 Institute of Mathematics Hanoi

  • Farhadinia B (2013) Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inf Sci 240:129–144

    Article  MathSciNet  MATH  Google Scholar 

  • Garg H, Rani D (2019) Some results on information measures for complex intuitionistic fuzzy sets. Int J Intell Syst 34(10):2319–2363

    Article  Google Scholar 

  • Goguen JA (1967) L-fuzzy sets. J Math Anal Appl 18(1):145–174

    Article  MathSciNet  MATH  Google Scholar 

  • Liu P, Liu J (2018) Some q-rung orthopai fuzzy Bonferroni mean operators and their application to multi-attribute group decision making. Int J Intell Syst 33(2):315–347

    Article  Google Scholar 

  • Liu P, Ali Z, Mahmood T (2020) The distance measures and cross-entropy based on complex fuzzy sets and their application in decision making. J Intell Fuzzy Syst 39(3):3351–3374

    Article  Google Scholar 

  • Mahmood T (2020) A novel approach towards bipolar soft sets and their applications. J Math, 2020, Article ID: 4690808

  • Mahmood T, Ullah K, Khan Q, Jan N (2019) An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Comput Appl 31(11):7041–7053

    Article  Google Scholar 

  • Mandal P, Ranadive AS (2019) Hesitant bipolar-valued fuzzy sets and bipolar-valued hesitant fuzzy sets and their applications in multi-attribute group decision making. Granul Comput 4(3):559–583

    Article  Google Scholar 

  • Miyamoto S (2005) Remarks on basics of fuzzy sets and fuzzy multisets. Fuzzy Sets Syst 156(3):427–431

    Article  MathSciNet  MATH  Google Scholar 

  • Mukherjee S (2012) Dijkstra’s algorithm for solving the shortest path problem on networks under intuitionistic fuzzy environment. J Math Modell Algorith 11(4):345–359

    Article  MathSciNet  MATH  Google Scholar 

  • Riaz M, Hashmi MR (2019) Linear Diophantine fuzzy set and its applications towards multi-attribute decision-making problems. J Intell Fuzzy Syst 37(4):5417–5439

    Article  Google Scholar 

  • Riaz M, Hashmi MR, Kalsoom H, Pamucar D, Chu YM (2020) Linear Diophantine fuzzy soft rough sets for the selection of sustainable material handling equipment. Symmetry 12(8):1215–1229

    Article  Google Scholar 

  • Riaz M, Hashmi MR, Pamucar D, Chu YM (2021a) Spherical linear Diophantine fuzzy sets with modeling uncertainties in MCDM. Comput Model Eng Sci 126(3):1125–1164

    Google Scholar 

  • Riaz M, Farid HMA, Aslam M, Pamucar D, Bozanić D (2021b) Novel approach for third-party reverse logistic provider selection process under linear diophantine fuzzy prioritized aggregation operators. Symmetry 13(7):1152–1178

    Article  Google Scholar 

  • Rodríguez RM, Bedregal B, Bustince H, Dong YC, Farhadinia B, Kahraman C, Herrera F (2016) A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making Towards High Quality Progress. Inf Fus 29:89–97

    Article  Google Scholar 

  • Singh P (2015) Correlation coefficients for picture fuzzy sets. J Intell Fuzzy Syst 28(2):591–604

    Article  MathSciNet  MATH  Google Scholar 

  • Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539

    MATH  Google Scholar 

  • Ullah K, Ali Z, Jan N, Mahmood T, Maqsood S (2018) Multi-attribute decision making based on averaging aggregation operators for picture hesitant fuzzy sets. Tech J 23(04):84–95

    Google Scholar 

  • Wang R, Li Y (2018) Picture hesitant fuzzy set and its application to multiple criteria decision-making. Symmetry 10(7):295–319

    Article  Google Scholar 

  • Wei G (2017) Picture fuzzy aggregation operators and their application to multiple attribute decision making. J Intell Fuzzy Syst 33(2):713–724

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Xia M, Xu Z, Zhu B (2013) Geometric Bonferroni means with their application in multi-criteria decision making. Knowl-Based Syst 40:88–100

    Article  Google Scholar 

  • Xu Z, Chen Q (2011) A multi-criteria decision making procedure based on interval-valued intuitionistic fuzzy bonferroni means. J Syst Sci Syst Eng 20(2):217–228

    Article  Google Scholar 

  • Xu Z, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35(4):417–433

    Article  MathSciNet  MATH  Google Scholar 

  • Xu Z, Yager RR (2010) Intuitionistic fuzzy Bonferroni means. IEEE Trans Syst Man Cybern Part B Cybern 41(2):568–578

    Google Scholar 

  • Yager RR (2009) On generalized Bonferroni mean operators for multi-criteria aggregation. Int J Approx Reason 50(8):1279–1286

    Article  MathSciNet  MATH  Google Scholar 

  • Yang Y, Hu J, Liu Y, Chen X (2019) Alternative selection of end-of-life vehicle management in China: a group decision-making approach based on picture hesitant fuzzy measurements. J Clean Prod 206:631–645

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  • Zhou W, He JM (2012) Intuitionistic fuzzy geometric Bonferroni means and their application in multicriteria decision making. Int J Intell Syst 27(12):995–1019

    Article  Google Scholar 

  • Zhu B, Xu Z, Xia M (2012) Hesitant fuzzy geometric Bonferroni means. Inf Sci 205:72–85

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan

    Tahir Mahmood, Muhammad Ahsen & Zeeshan Ali

Authors
  1. Tahir Mahmood
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Muhammad Ahsen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zeeshan Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tahir Mahmood.

Ethics declarations

Conflict of interest

We declare that we do have no commercial or associative interests that represent a conflict of interests in connection with this manuscript. There are no professional or other personal interests that can inappropriately influence our submitted work.

Research involving human participants and/or animals

This article does not contain any studies with human participants or animals performed by any of the authors.

Data availability statement

The data used in this manuscript are available to all and anyone can use it without prior permission of the authors by just citing this article.

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

Mahmood, T., Ahsen, M. & Ali, Z. Multi-attribute group decision-making based on Bonferroni mean operators for picture hesitant fuzzy numbers. Soft Comput 25, 13315–13351 (2021). https://doi.org/10.1007/s00500-021-06172-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-021-06172-8

Keywords

Search

Navigation