Skip to main content
Log in

Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weight

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

Abstract

Reasonable and effective assessment of express service quality can help express company discover its own shortcomings and overcome them, which is crucial significant to enhance its service quality. When considering the decision assessment of express company, the key issue that emerge powerful ambiguity. Pythagorean fuzzy set as an efficient math tool can capture the indeterminacy successfully. The major focus of this manuscript is to explore various interactive Hamacher power aggregation operators for Pythagorean fuzzy numbers. Firstly, we defined novel interactive Hamacher operation, on this basis we presented some Pythagorean fuzzy interactive Hamacher power aggregation operators such as Pythagorean fuzzy interactive Hamacher power average, weighted average (PFIHPWA), ordered weighted average, Pythagorean fuzzy interactive Hamacher power geometric, weighted geometric (PFIHPWG) and ordered geometric operators,respectively. Meanwhile, we verified their general properties and specific cases as well. The salient feature of proposed operators is that they can not only reduce the impact of negative data and consider the interactions between membership and nonmembership degrees, but also provide more general results through a parameter. Secondly, we defined a Pythagorean fuzzy entropy measure, and then establish a method to determine the attribute weights. Further, based on the conceived PFIHPWA and PFIHPWG operators we explored a novel approach to manage multiple attribute decision making problems. At last, the proposed techniques are carried out in a real application concerning on the assessment of express service quality to display the applicability and effectiveness, as well as the influence of changed parameters on the results. In addition, its advantages are displayed by a systematic comparison with relevant approaches.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Akram M, Ilyas F, Garg H (2020) Multi-criteria group decision making based on ELECTRE-I method on Pythagorean fuzzy information. Soft Comput 24(5):3425–3453

    Article  Google Scholar 

  • Athira TM, John SJ, Garg H (2020) A novel entropy measure of Pythagorean fuzzy soft sets. AIMS Math 5(2):1050–1061

    Article  MathSciNet  Google Scholar 

  • Chen T (2018) An effective correlation-based compromise approach for multiple criteria decision analysis with Pythagorean fuzzy information. J Intell Fuzzy Syst 35(3):3529–3541

    Article  Google Scholar 

  • Fan X, Zheng M (2012) Empirical analysis of express service quality based on fuzzy comprehensive evaluation. Appl Mech Mater 121:4456–4460

    Google Scholar 

  • Gao H (2018) Pythagorean fuzzy Hamacher prioritized aggregation operators in multiple attribute decision making. J Intell Fuzzy Syst 35:2229–2245

    Article  Google Scholar 

  • Gao H, Lu M, Wei GW, Wei Y (2018) Some novel Pythagorean fuzzy interaction aggregation operators in multiple attribute decision making. Fund Inform 159:385–428

    MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Garg H (2016) Some series of intuitionistic fuzzy interactive averaging aggregation operators. Springer Plus 5(1):1–27

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Garg H (2018a) Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision-making process. Int J Intell Syst 33(1):1234–1263

    Article  Google Scholar 

  • Garg H (2018b) 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 (2018c) Generalised Pythagorean fuzzy geometric interactive aggregation operators using Einstein operations and their application to decision making. J Exp Theor Artif Intell 30(6):763–794

    Article  Google Scholar 

  • Garg H (2019a) Neutrality operations-based Pythagorean fuzzy aggregation operators and its applications to multiple attribute group decision-making process. J Ambient Intell Human Comput. https://doi.org/10.1007/s12652-019-01448-2

    Article  Google Scholar 

  • Garg H (2019b) Novel neutrality operations based Pythagorean fuzzy geometric aggregation operators for multiple attribute group decision analysis. Int J Intell Syst 34(10):2459–2489

    Article  Google Scholar 

  • Garg H (2020) A novel trigonometric operation-based q-rung orthopair fuzzy aggregation operators and its fundamental properties. Neural Comput Appl. https://doi.org/10.1007/s00521-020-04859-x

    Article  Google Scholar 

  • Garg H, Kaur G (2020) Quantifying gesture information in brain hemorrhage patients using probabilistic dual hesitant fuzzy sets with unknown probability information. Comput Ind Eng 140:106211. https://doi.org/10.1016/j.cie.2019.106211

    Article  Google Scholar 

  • Grabisch M, Marichal JL, Mesiar R, Pap E (2009) Aggregation functions. Encyclopedia of mathematics and its applications, vol 127. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Grabisch M, Marichal JL, Mesiar R, Pap E (2011) Aggregation functions: means. Inf Sci 181:1–22

    Article  MathSciNet  MATH  Google Scholar 

  • Hamachar H (1978) Uber logische verknunpfungenn unssharfer Aussagen und deren Zugenhorige Bewertungsfunktione Trappl. Progr Cybern Syst Res 3:276–288

    Google Scholar 

  • Khan AA, Ashraf S, Abdullah S, Qiyas M, Luo J, Khan SU (2019) Pythagorean fuzzy Dombi aggregation operators and their application in decision support system. Symmetry 11:383. https://doi.org/10.3390/sym11030383

    Article  MATH  Google Scholar 

  • Klement EP, Mesiar R, Pap E (2000) Triangular norms, trends in logics. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  • Klement EP, Mesiar R, Pap E (2004) Triangular norms II: general constructions and parameterized families. Fuzzy Sets Syst 145:411–438

    Article  MathSciNet  MATH  Google Scholar 

  • Li N, Garg H, Wang L (2019) Some novel interactive hybrid weighted aggregation operators with Pythagorean fuzzy numbers and their applications to decision making. Mathematics 7(12):1150

    Article  Google Scholar 

  • Li Y, Garg H, Deng Y (2020) A new uncertainty measure of discrete Z-numbers. Int J Fuzzy Syst 22(3):760–776

    Article  MathSciNet  Google Scholar 

  • Liang D, Xu Z (2017) The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets. Appl Soft Comput 60:167–179

    Article  Google Scholar 

  • Liang D, Zhang Y, Xu Z, Jamaldeen A (2019a) Pythagorean fuzzy VIKOR approaches based on TODIM for evaluating internet banking website quality of Ghanaian banking industry. Appl Soft Comput 78:583–594

    Article  Google Scholar 

  • Liang DC, Darko AP, Xu ZS (2019b) Pythagorean fuzzy partitioned geometric Bonferroni mean and its application to multi-criteria group decision making with grey relational analysis. Int J Fuzzy Syst 21(1):115–128

    Article  MathSciNet  Google Scholar 

  • Liu M, Ren H (2015) A study of multi-attribute decision making based on a new intuitionistic fuzzy entropy measure. Syst Eng Theory Pract 35(11):2909–2916

    Google Scholar 

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

    Article  Google Scholar 

  • Meshram SG, Alvandi E, Singh VP, Meshram C (2019) Comparison of AHP and fuzzy AHP models for prioritization of watersheds. Soft Comput 23(24):13615–13625

    Article  Google Scholar 

  • Peng XD, Dai JG (2017) Approaches to Pythagorean fuzzy stochastic multi-criteria decision making based on prospect theory and regret theory with new distance measure and score function. Int J Intell Syst 32(11):1187–1214

    Article  Google Scholar 

  • Peng XD, Dai JG (2019) Research on the assessment of classroom teaching quality with q-rung orthopair fuzzy information based on multiparametric similarity measure and combinative distance-based assessment. Int J Intell Syst 34:1588–1630

    Article  Google Scholar 

  • Peng XD, Garg H (2019) Multiparametric similarity measures on Pythagorean fuzzy sets with applications to pattern recognition. Appl Intell 49:4058–4096

    Article  Google Scholar 

  • Peng XD, Liu L (2019) Information measures for q-rung orthopair fuzzy sets. Int J Intell Syst 34(8):1795–1834

    Article  Google Scholar 

  • Peng XD, Selvachandran G (2019) Pythagorean fuzzy set: state of the art and future directions. Artif Intell Rev 52(3):1873–1927

    Article  Google Scholar 

  • Perez L, Rodrguez-Picn L, Alvarado-Iniesta A, Luviano Cruz D, Xu Z (2018) MOORA under Pythagorean fuzzy set for multiple criteria decision making. Complexity 5:1–10. https://doi.org/10.1155/2018/2602376

    Article  MATH  Google Scholar 

  • Qin J (2017) Generalized Pythagorean fuzzy maclaurin symmetric means and its application to multiple attribute SIR group decision model. Int J Fuzzy Syst 20(1):1–15

    MathSciNet  Google Scholar 

  • Wang L, Li N (2019) Continuous interval-valued Pythagorean fuzzy aggregation operators for multiple attribute group decision making. J Intell Fuzzy Syst 36:6245–6263

    Article  Google Scholar 

  • Wang L, Li N (2020) Pythagorean fuzzy interaction power Bonferroni mean aggregation operators in multiple attribute decision making. Int J Intell Syst 35(1):150–183

    Article  Google Scholar 

  • Wei GW (2017) Pythagorean fuzzy interaction aggregation operators and their application to multiple attribute decision making. Int J Fuzzy Syst 33(4):2119–2132

    MATH  Google Scholar 

  • Wei GW (2019) Pythagorean fuzzy Hamacher power aggregation operators in multiple attribute decision making. Fund Inf 166:57–85

    MathSciNet  MATH  Google Scholar 

  • Wei GW, Lu M (2018) Pythagorean fuzzy power aggregation operators in multiple attribute decision making. Int J Intell Syst 33:169–186

    Article  Google Scholar 

  • Wu SJ, Wei GW (2017) Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Int J Knowl Based Intell Eng Syst 21(3):189–201

    Google Scholar 

  • Xu Z, Yager RR (2010) Power-geometric operators and their use in group decision making. IEEE Trans Fuzzy Syst 18(1):94–105

    Article  Google Scholar 

  • Xu Q, Yu K, Zeng S, Liu J (2017) Pythagorean fuzzy induced generalized OWA operator and its application to multi-attribute group decision-making. Int J Innov Comput I(13):1527–1536

    Google Scholar 

  • Yager RR (2001) The power average operator. IEEE Trans Syst Man Cybern A 31(6):724–731

    Article  Google Scholar 

  • Yager RR (2013) Pythagorean fuzzy subsets. In: Proceedings of the 2013 joint IFSA world congress and NAFIPS annual meeting

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

    Article  Google Scholar 

  • Yang MS, Hussain Z (2018) Fuzzy entropy for Pythagorean fuzzy sets with application to multicriterion decision making. Complexity. https://doi.org/10.1155/2018/2832839

    Article  MATH  Google Scholar 

  • Yang W, Pang Y (2018) New Pythagorean fuzzy interaction Maclaurin symmetric mean operators and their application in multiple attribute decision making. IEEE Access 6:39241–39260

    Article  Google Scholar 

  • Zeng S, Mu Z, Balezentis T (2018) A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making. Int J Intell Syst 33(3):573–585

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Zhang XL (2018) A novel approach based on similarity measure for Pythagorean fuzzy multiple attribute group decision making. Int J Intell Syst 31(6):593–611

    Article  Google Scholar 

  • Zhang XL, Xu ZS (2014) Extension of TOPSIS to multiple attribute decision making with Pythagorean fuzzy sets. Int J Intell Syst 29:1061–1078

    Article  Google Scholar 

  • Zhu X, Bai K, Wang J, Zhang R, Xing Y (2019) Pythagorean fuzzy interaction power partitioned Bonferroni means with applications to multi-attribute group decision making. J Intell Fuzzy Syst 36:3423–3438

    Article  Google Scholar 

  • Zhuang D, Li J, Xia Y (2015) An evaluation of courier enterprises service quality by using CZIPA approach. J Beijing Technol Bus Univ 30(2):48–55

    Google Scholar 

Download references

Acknowledgements

The authors are very grateful to the anonymous reviewers for their valuable comments and constructive suggestions that greatly improved the quality of this paper. The work was partly supported by the Scientific Research Funds Project of Liaoning Province Education Department (No. LJ2019QL014), Doctor Startup Foundation of Liaoning Province (No. 20170520075).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lei Wang.

Ethics declarations

Conflict of interest

The authors declare no conflict of interests regarding the publication for the paper.

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

Wang, L., Garg, H. & Li, N. Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weight. Soft Comput 25, 973–993 (2021). https://doi.org/10.1007/s00500-020-05193-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-020-05193-z

Keywords

Navigation