Skip to main content
SpringerLink
Log in

Some novel interval-valued Pythagorean fuzzy aggregation operator based on Hamacher triangular norms and their application in MADM issues

  • Published:
Computational and Applied Mathematics Aims and scope Submit manuscript

Abstract

The motivation of this paper is to build up a new technique to manage multi-attribute decision-making (MADM) issues with interval-valued Pythagorean fuzzy (IVPF) set according to the concepts of Hamacher t-norm and t-conorm, and give its application in MADM problems. To begin with, we integrate the Hamacher operations on IVPF sets. Then, in view of these operations, we formulate a few IVPF aggregation operators, for example, IVPF Hamacher weighted average operator, IVPF Hamacher order weighted average operator, IVPF Hamacher hybrid average operator, IVPF Hamacher weighted geometric operator, IVPF Hamacher order weighted geometric operator, and IVPF Hamacher hybrid geometric operator. We investigate the distinguished features of these suggested operators. Moreover, we carry out the proposed aggregation operators to produce a method for solving MADM issues under IVPF data. We present an example of the emerging software system selection to elaborate on its practicality and effectiveness. We investigate the impact of the parameter for different values on decision-making outcomes. The main advantage of utilizing the suggested operator lies in the fact that this operator provides an increasingly complete perspective on the issue to the decision-makers. The technique suggested in this study gives progressively broad, improve the accuracy and exact outcomes when contrasted with the existing related methods. Therefore, this technique performs an important function in real-life MADM issues.

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

Similar content being viewed by others

References

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

    Google Scholar 

  • Chen TY (2018) An interval-valued Pythagorean fuzzy outranking method with a closeness-based assignment model for multiple criteria decision making. Int J Intell Syst 33(1):126–168

    Google Scholar 

  • Chen ZS, Chin KS, Li YL, Yang Y (2016) Proportional hesitant fuzzy linguistic term set for multiple criteria group decision making. Inf Sci 357:61–87

    MathSciNet  MATH  Google Scholar 

  • Chen ZS, Yang Y, Wang XJ, Chin KS, Tsui KL (2019) Fostering linguistic decision-making under uncertainty: A proportional interval type-2 hesitant fuzzy TOPSIS approach based on Hamacher aggregation operators and andness optimization models. Inf Sci 500:229–258

    Google Scholar 

  • Chen ZS, Liu XL, Rodríguez RM, Wang XJ, Chin KS, Tsui KL, Martínez L (2020) Identifying and prioritizing factors affecting in-cabin passenger comfort on high-speed rail in China: a fuzzy-based linguistic approach. Appl Soft Comput 95

  • Chen ZS, Liu XL, Chin KS, Pedrycz W, Tsui KL, Skibniewski MJ (2021) Online-review analysis based large-scale group decision-making for determining passenger demands and evaluating passenger satisfaction: Case study of high-speed rail system in China. Inf Fus 69:22–39

    Google Scholar 

  • Deschrijver G, Cornelis C, Kerre EE (2004) On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE T Fuzzy Syst 12:45–61

    MATH  Google Scholar 

  • Dey A, Senapati T, Pal M, Chen G (2020) A novel approach to hesitant multi-fuzzy soft set based decision-making. AIMS Math 5(3):1985–2008

    MathSciNet  Google Scholar 

  • Du Y, Hou F, Zafar W, Yu Q, Zhai Y (2017) A novel method for multiattribute decision making with interval-valued Pythagorean fuzzy linguistic information. Int J Intell Syst 32(10):1085–1112

    Google Scholar 

  • Garg H (2016) 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

    MATH  Google Scholar 

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

    Google Scholar 

  • Hamachar H (1978) Uber logische verknunpfungenn unssharfer Aussagen und deren Zugenhorige Bewertungsfunktione Trappl, Progress in Cybernatics and Systems Research, K. Riccardi, eds 3:276–288

  • Huang YH, Wei GW (2018) TODIM method for interval-valued Pythagorean fuzzy multiple attribute decision making. Int J Knowl Based Intell Eng Syst 22:249–259

    Google Scholar 

  • Jana C, Pal M (2018) Assessment of enterprise performance based on picture fuzzy Hamacher aggregation operators. Symmetry 11(1):75. https://doi.org/10.3390/sym11010075

    Article  MATH  Google Scholar 

  • Jana C, Senapati T, Pal M, Yager RR (2019) Picture fuzzy Dombi aggregation operators: application to MADM process. Appl Soft Comput 74:99–109

    Google Scholar 

  • Jana C, Senapati T, Pal M (2019) Pythagorean fuzzy Dombi aggregation operators and its applications in multiple attribute decision-making. Int J Intell Syst 34(9):2019–2038

    Google Scholar 

  • Jana C, Muhiuddin G, Pal M (2020) Multiple-attribute decision making problems based on SVTNH methods. J Ambient Intell Hum Comput 11:3717–3733

    Google Scholar 

  • Li Z, Wei G, Gao H (2018) Methods for multiple attribute decision making with interval-valued Pythagorean fuzzy information. Mathematics 6:228. https://doi.org/10.3390/math6110228

    Article  MATH  Google Scholar 

  • Li Z, Wei G, Lu M (2018) Pythagorean fuzzy hamy mean operators in multiple attribute group decision making and their application to supplier selection. Symmetry-Basel 10(10):505

    Google Scholar 

  • Liang D, Darko AP, Xu Z (2018) Interval-valued Pythagorean fuzzy extended Bonferroni mean for dealing with heterogenous relationship among attributes. Int J Intell Syst 33(7):1381–1411

    Google Scholar 

  • Liu P (2014) Some hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making. IEEE Trans Fuzzy Syst 22(1):83–97

    Google Scholar 

  • Lu M, Wei G, Alsaadi FE, Hayat T, Alsaedi A (2017) Hesitant Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. J Intell Fuzzy Syst 33(2):1105–1117

    MATH  Google Scholar 

  • Lu J, He T, Wei G, Wu J, Wei C (2020) Cumulative prospect theory: performance evaluation of Government purchases of home-based elderly-care services using the Pythagorean 2-tuple linguistic TODIM method. Int J Environ Res Public Health 17(6):1939

    Google Scholar 

  • Peng X, Yang Y (2016) Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators. Int J Intell Syst 31(5):444–487

    Google Scholar 

  • Rahman K, Abdullah S (2019) Some induced generalized interval-valued Pythagorean fuzzy Einstein geometric aggregation operators and their application to group decision-making. Comput Appl Math 38(3):139

    MathSciNet  MATH  Google Scholar 

  • Rahman K, Abdullahb S (2019) Some new generalized interval-valued Pythagorean fuzzy aggregation operators using Einstein \(t\)-norm and \(t\)-conorm. J Intell Fuzzy Syst 37(3):3721–3742

    Google Scholar 

  • Rahman K, Abdullah S, Shakeel M, Sajjad Ali Khan M, Ullah M (2017) Interval-valued Pythagorean fuzzy geometric aggregation operators and their application to group decision making problem. Cogent Math 4:1338638

    MathSciNet  MATH  Google Scholar 

  • Rahman K, Ali A, Abdullah S, Amin F (2018) Approaches to multi-attribute group decision making based on induced interval-valued Pythagorean fuzzy Einstein aggregation operator. New Math Nat Comput 14(3):343–361

    MathSciNet  MATH  Google Scholar 

  • Rahman K, Abdullah S, Ali A, Amin F (2019) Interval-valued Pythagorean fuzzy Einstein hybrid weighted averaging aggregation operator and their application to group decisionmaking. Complex Intell Syst 5:41–52

    Google Scholar 

  • Roychowdhury S, Wang BH (1998) On generalized Hamacher families of triangular operators. Int J Approx Reason 19:419–439

    MathSciNet  MATH  Google Scholar 

  • Sajjad Ali Khan M, Abdullah S, Ali MY, Hussain I, Farooq M (2018) Extension of TOPSIS method base on Choquet integral under interval-valued Pythagorean fuzzy environment. J Intell Fuzzy Syst 34(1):267–282

    Google Scholar 

  • Senapati T, Yager RR (2019) Some new operations over Fermatean fuzzy numbers and application of Fermatean fuzzy WPM in multiple criteria decision making. Informatica 30(2):391–412

    Google Scholar 

  • Senapati T, Yager RR (2019) Fermatean fuzzy weighted averaging/geometric operators and its application in multi-criteria decision-making methods. Eng Appl Artif Intell 85:112–121

    Google Scholar 

  • Senapati T, Yager RR (2020) Fermatean fuzzy sets. J Ambient Intell Human Comput 11(2):663–674

    Google Scholar 

  • Senapati T, Yager RR, Chen G (2020) Cubic intuitionistic WASPAS technique and its application in multi-criteria decision-making. J Ambient Intell Human Comput. https://doi.org/10.1007/s12652-020-02667-8

    Article  Google Scholar 

  • Tan C, Yi W, Chen X (2015) Hesitant fuzzy Hamacher aggregation operators for multicriteria decision making. Appl Soft Comput 26:325–349

    Google Scholar 

  • Tang XY, Wei GW, Gao H (2019) Models for multiple attribute decision making with interval-valued pythagorean fuzzy Muirhead mean operators and their application to green suppliers selection. Informatica 30(1):153–186

    Google Scholar 

  • Wang TC, Lee HD (2009) Developing a fuzzy TOPSIS approach based on subjective weights and objective weights. Expert Syst Appl 36:8980–8985

    Google Scholar 

  • Wei G, Lu M, Tang X, Wei Y (2018) Pythagorean hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Int J Intell Syst 33(6):1197–1233

    Google Scholar 

  • Wei G, Garg H, Gao H, Wei C (2018) Interval-valued pythagorean fuzzy Maclaurin symmetric mean operators in multiple attribute decision making. IEEE Access 6:67866–67884

    Google Scholar 

  • Wei G, Tang Y, Zhao M, Lin R, Wu J (2020) Selecting the low-carbon tourism destination: based on Pythagorean fuzzy taxonomy method. Mathematics 8(5):832

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    MATH  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

    Google Scholar 

  • Zhang X (2018) Pythagorean fuzzy clustering analysis: a hierarchical clustering algorithm with the ratio index-based ranking methods. Int J Intell Syst 33(9):1798–1822

    Google Scholar 

  • Zhou LY, Zhao XF, Wei GW (2014) Hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. J Intell Fuzzy Syst 26(6):2689–2699

    MathSciNet  MATH  Google Scholar 

Download references

Funding

Financial support offered by National Natural Science Foundation of China (Grant no-12071376) is thankfully acknowledged.

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Beibei, Chongqing, 400715, China

    Tapan Senapati & Guiyun Chen

Authors
  1. Tapan Senapati
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guiyun Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tapan Senapati.

Additional information

Communicated by Anibal Tavares de Azevedo.

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

Senapati, T., Chen, G. Some novel interval-valued Pythagorean fuzzy aggregation operator based on Hamacher triangular norms and their application in MADM issues. Comp. Appl. Math. 40, 109 (2021). https://doi.org/10.1007/s40314-021-01502-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40314-021-01502-w

Keywords

Mathematics Subject Classification

Search

Navigation