Skip to main content
SpringerLink
Log in

Some q-rung orthopair fuzzy point weighted aggregation operators for multi-attribute decision making

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

q-Rung orthopair fuzzy sets, originally proposed by Yager, can dynamically adjust the range of indication of decision information by changing a parameter q based on the different hesitation degree, and point operator is a useful aggregation technology that can control the uncertainty of valuating data from some experts and thus get intensive information in the process of decision making. However, the existing point operators are not available for decision-making problems under q-Rung orthopair fuzzy environment. Thus, in this paper, we firstly propose some new point operators to make it conform to q-rung orthopair fuzzy numbers (q-ROFNs). Then, associated with classic arithmetic and geometric operators, we propose a new class of point weighted aggregation operators to aggregate q-rung orthopair fuzzy information. These proposed operators can redistribute the membership and non-membership in q-ROFNs according to different principle. Furthermore, based on these operators, a novel approach to multi-attribute decision making (MADM) in q-rung orthopair fuzzy context is introduced. Finally, we give a practical example to illustrate the applicability of the new approach. The experimental results show that the novel MADM method outperforms the existing MADM methods for dealing with MADM problems.

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
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Arora R, Garg H (2018) Prioritized averaging/geometric aggregation operators under the intuitionistic fuzzy soft set environment. Sci Iran. https://doi.org/10.24200/sci.2017.4410

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Garg H (2016a) A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems. Appl Soft Comput 38:988–999

    Article  Google Scholar 

  • Garg H (2016b) Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making. Comput Ind Eng 101:53–69

    Article  Google Scholar 

  • Garg H (2016c) Generalized intuitionistic fuzzy multiplicative interactive geometric operators and their application to multiple criteria decision making. Int J Mach Learn Cybern 7(6):1075–1092

    Article  Google Scholar 

  • Garg H (2016d) A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. Int J Intell Syst 31(9):886–920

    Article  Google Scholar 

  • Garg H (2016e) A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multi-criteria decision making problem. J Intell Fuzzy Syst 31(1):529–540

    Article  Google Scholar 

  • Garg H (2017a) Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multi-criteria decision making process. Int J Intell Syst 32(6):597–630

    Article  Google Scholar 

  • Garg H (2017b) A new improved score function of an interval-valued Pythagorean fuzzy set based TOPSIS method. Int J Uncertain Quantif 7(5):463–474

    Article  Google Scholar 

  • Garg H (2018a) Some methods for strategic decision-making problems with immediate probabilities in Pythagorean fuzzy environment. Int J Intell Syst 33(4):687–712

    Article  Google Scholar 

  • Garg H (2018b) Generalized Pythagorean fuzzy geometric interactive aggregation operators using Einstein operations and their application to decision making. J Exp Theor Artif Int. https://doi.org/10.1080/0952813x.2018.1467497

    Article  Google Scholar 

  • Garg H (2018c) New exponential operational laws and their aggregation operators for interval-valued pythagorean fuzzy multi-criteria decision-making. Int J Intell Syst 33(3):653–683

    Article  Google Scholar 

  • Garg H (2018d) Linguistic Pythagorean fuzzy sets and its applications in multi attribute decision making process. Int J Intell Syst 33(6):1234–1263

    Article  Google Scholar 

  • Garg H (2018e) Hesitant Pythagorean fuzzy sets and their aggregation operators in multiple-attribute decision-making. Int J Uncertain Quantif 8(3):267–289

    Article  MathSciNet  Google Scholar 

  • Garg H (2018f) A linear programming method based on an improved score function for interval-valued Pythagorean fuzzy numbers and its application to decision-making. Int J Uncertain Fuzziness Knowl-Based Syst 29(1):67–80

    Article  MathSciNet  Google Scholar 

  • He YD, Chen HY, He Z, Zhou LG (2015) Multi-attribute decision making based on neutral averaging operators for intuitionistic fuzzy information. Appl Soft Comput 27:64–76

    Article  Google Scholar 

  • He YD, He Z, Huang H (2017) Decision making with the generalized intuitionistic fuzzy power interaction averaging operators. Soft Comput 21(5):1129–1144

    Article  Google Scholar 

  • Ju YB, Liu XY, Ju DW (2016) Some new intuitionistic linguistic aggregation operators based on Maclaurin symmetric mean and their applications to multiple attribute group decision making. Soft Comput 20(11):4521–4548

    Article  Google Scholar 

  • Khaleie S, Fasanghari M (2012) An intuitionistic fuzzy group decision making method using entropy and association coefficient. Soft Comput 16(7):1197–1211

    Article  Google Scholar 

  • Le HS (2016) Generalized picture distance measure and applications to picture fuzzy clustering. Appl Soft Comput 46:284–295

    Article  Google Scholar 

  • Liang DC, Xu ZS, Darko AP (2017) Projection model for fusing the information of Pythagorean fuzzy multi-criteria group decision making based on geometric Bonferroni mean. Int J Intell Syst 32(9):966–987

    Article  Google Scholar 

  • Liu PD, Li DF (2017) Some Muirhead mean operators for intuitionistic fuzzy numbers and their applications to group decision making. PLoS ONE 12(1):e0168767

    Article  Google Scholar 

  • Liu PD, Liu JL (2017) 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  MathSciNet  Google Scholar 

  • Liu HW, Wang GJ (2007) Multi-criteria decision-making methods based on intuitionistic fuzzy sets. Eur J Oper Res 179:220–233

    Article  Google Scholar 

  • Liu PD, Wang P (2017) Some q-rung orthopair fuzzy aggregation operators and their applications to multi-attribute group decision making. Int J Intell Syst 33(2):259–280

    Article  Google Scholar 

  • Liu PD, Chen SM, Liu J (2017) Some intuitionistic fuzzy interaction partitioned Bonferroni mean operators and their application to multi-attribute group decision making. Inf Sci 411:98–121

    Article  Google Scholar 

  • Ma ZM, Xu ZS (2016) Symmetric Pythagorean fuzzy weighted geometric/averaging operators and their application in multi-criteria decision making problems. Int J Intell Syst 31(12):1198–1219

    Article  Google Scholar 

  • Mohammadi SE, Makui A (2017) Multi-attribute group decision making approach based on interval-valued intuitionistic fuzzy sets and evidential reasoning methodology. Soft Comput 21:5061–5080

    Article  Google Scholar 

  • Peng XD, Yuan HY (2016) Fundamental properties of Pythagorean fuzzy aggregation operators. Fund Inform 147(4):415–446

    Article  MathSciNet  Google Scholar 

  • Peng XD, Dai JG, Garg H (2018) Exponential operation and aggregation operator for q-rung orthopair fuzzy set and their decision-making method with a new score function. Int J Intell Syst 33(11):2255–2282

    Article  Google Scholar 

  • Wan SP, Yi ZH (2016) Power average of trapezoidal intuitionistic fuzzy numbers using strict t-norms and t-conorms. IEEE Trans Fuzzy Syst 24(5):1035–1047

    Article  Google Scholar 

  • Xia MM (2015) Point operators for intuitionistic multiplicative information. J Intell Fuzzy Syst 28:615–620

    MathSciNet  MATH  Google Scholar 

  • Xia MM, Xu ZS (2010) Generalized point operators for aggregating intuitionistic fuzzy information. Int J Intell Syst 25(11):1061–1080

    MATH  Google Scholar 

  • Xing YP, Zhang RT, Xia MM, Wang J (2017) Generalized point aggregation operators for dual hesitant fuzzy information. J Intell Fuzzy Syst 33(1):515–527

    Article  Google Scholar 

  • Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6):1179–1187

    Article  Google Scholar 

  • Yager RR (2014) Pythagorean membership grades in multi-criteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965

    Article  Google Scholar 

  • Yager RR (2018) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 26(5):1222–1230

    Article  Google Scholar 

  • Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers, and decision making. Int J Intell Syst 28(5):436–452

    Article  Google Scholar 

  • Yager RR, Alajlan N (2017) Approximate reasoning with generalized orthopair fuzzy sets. Inform Fusion 38:65–73

    Article  Google Scholar 

  • Zhang X (2016) Multicriteria Pythagorean fuzzy decision analysis: a hierarchical QUALIFLEX approach with the closeness index-based ranking methods. Inf Sci 330:104–124

    Article  Google Scholar 

Download references

Acknowledgements

This work was partially supported by a key program of the National Natural Science Foundation of China (No. 71532002) and Fundamental Research Funds for the Central Universities (No. 2017YJS067) and Beijing Logistics Informatics Research Base.

Author information

Authors and Affiliations

  1. School of Economics and Management, Beijing Jiaotong University, Beijing, China

    Yuping Xing, Runtong Zhang & Jun Wang

  2. School of Management, Capital Normal University, Beijing, China

    Zhen Zhou

Authors
  1. Yuping Xing
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Runtong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhen Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Runtong Zhang.

Ethics declarations

Conflict of interest

The authors declare that there are no conflicts of interest to this work.

Ethical approval

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

Additional information

Communicated by V. Loia.

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

Xing, Y., Zhang, R., Zhou, Z. et al. Some q-rung orthopair fuzzy point weighted aggregation operators for multi-attribute decision making. Soft Comput 23, 11627–11649 (2019). https://doi.org/10.1007/s00500-018-03712-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-018-03712-7

Keywords

Search

Navigation