Skip to main content

Advertisement

Springer Nature Link
Log in

Another View on Intuitionistic Fuzzy Preference Relation-Based Aggregation Operators and Their Applications

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

Multi-attribute group decision making (\(\mathrm {MAGDM}\)) can be considered as the process of ranking alternatives or selecting an optimal alternative by many decision makers based on multiple criteria. By comparing any two alternatives pairwise, preference relations provide efficient ways to represent the preference degrees of decision makers. The aim of this paper is to introduce the notions of upward intuitionistic fuzzy preference relations from fuzzy information system and to study some properties of these relations. Further the series of upward intuitionistic fuzzy preference aggregation operators including the upward intuitionistic fuzzy preference weighted averaging \(\left( \mathrm {UIFPWA}\right) \) operator, upward intuitionistic fuzzy preference ordered weighted averaging \( \left( \mathrm {UIFPOWA}\right) \) operator and upward intuitionistic fuzzy preference hybrid averaging \(\left( \mathrm {UIFPHA}\right) \) operator and their related results are also investigated. We developed a \(\mathrm {MAGDM}\) method based on the proposed operators under the fuzzy environment and illustrated with a numerical example to study the applicability of the new approach on a candidate selection decision-making problem.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Zeng, S.Z., Cao, C.D., Deng, Y., Shen, X.D.: Pythagorean fuzzy information aggregation based on weighted induced operator and its application to R&D projections selection. Informatica 29, 567–580 (2018)

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  4. Shi, L.L., Ye, J.: Multiple attribute group decision-making method using correlation coefficients between linguistic neutrosophic numbers. J. Intell. Fuzzy Syst. 35, 917–925 (2018)

    Article  Google Scholar 

  5. Ye, J.: Correlation coefficients of interval neutrosophic hesitant fuzzy sets and its application in a multiple attribute decision making method. Informatica 27, 179–202 (2016)

    Article  Google Scholar 

  6. Wei, G.W., Wang, H.J., Lin, R.: Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information. Knowl. Inform. Syst. 26, 337–349 (2011)

    Article  Google Scholar 

  7. Zeng, W.Y., Li, D.Q., Yin, Q.: Distance and similarity measures of Pythagorean fuzzy sets and their applications to multiple criteria group decision making. Int. J. Intell. Syst. 33, 2236–2254 (2018)

    Article  Google Scholar 

  8. Wei, G.W., Gao, H.: The generalized dice similarity measures for picture fuzzy sets and their applications. Informatica 29, 107–124 (2018)

    Article  MathSciNet  Google Scholar 

  9. Wei, G.W.: TODIM method for picture fuzzy multiple attribute decision making. Informatica 29, 555–566 (2018)

    Article  MathSciNet  Google Scholar 

  10. Wang, J., Wei, G.W., Lu, M.: An extended VIKOR method for multiple criteria group decision making with triangular fuzzy neutrosophic numbers. Symmetry-Basel 10, 497 (2018)

    Article  Google Scholar 

  11. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–356 (1965)

    Article  Google Scholar 

  12. Atanassov, K.: More on intuitionistic fuzzy sets. Fuzzy Sets Syst. 33, 37–46 (1989)

    Article  MathSciNet  Google Scholar 

  13. Liang, Q., Liao, X., Liu, J.: A social ties-based approach for group decision-making problems with incomplete additive preference relations. Knowl. Based Syst. 119, 68–86 (2017)

    Article  Google Scholar 

  14. Atanassov, K., Pasi, G., Yager, R.R.: Intuitionistic fuzzy interpretations of multi-criteria multi-person and multimeasurement tool decision making. Int. J. Syst. Sci. 36, 859–868 (2005)

    Article  Google Scholar 

  15. Li, D.F.: Multiattribute decision making models and methods using intuitionistic fuzzy sets. J. Comput. Syst. Sci. 70, 73–85 (2005)

    Article  MathSciNet  Google Scholar 

  16. Wei, G.W.: Maximizing deviation method for multiple attribute decision making in intuitionistic fuzzy setting. Knowl. Based Syst. 21(8), 833–836 (2008)

    Article  Google Scholar 

  17. Yager, R.R., Abbasov, A.M.: Pythagorean membership grades, complex numbers, and decision making. Int. J. Intell. Syst. 28, 436–452 (2014)

    Article  Google Scholar 

  18. Zhang, X.L., Xu, Z.S.: Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int. J. Intell. Syst. 29, 1061–1078 (2014)

    Article  MathSciNet  Google Scholar 

  19. Yager, R. R.: Pythagorean fuzzy subsets. In: Proceedings of the joint IFSA world congress and NAFIPS annual meeting; June 24–28, Edmonton, Canada: pp. 57-61 (2013)

  20. Xu, Z.S.: Intuitionistic fuzzy aggregation operators. IEEE Trans. Fuzzy Syst. 15, 1179–1187 (2007)

    Article  Google Scholar 

  21. Zhao, H., Xu, Z.S., Ni, M.F., Liu, S.S.: Generalized aggregation operators for intuitionistic fuzzy sets. Int. J. Intell. Syst. 25, 1–30 (2010)

    Article  Google Scholar 

  22. Liu, P., Liu, J., Merigó, J.M.: Partitioned Heronian means based on linguistic intuitionistic fuzzy numbers for dealing with multi-attribute group decision making. Appl. Soft Comput. 62, 395–422 (2018)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  26. Garg, H.: Generalized Pythagorean fuzzy geometric aggregation operators using Einstein \(t\)-norm and \(t\)-conorm for multicriteria decision-making process. Int. J. Intell. Syst. 32(6), 597–630 (2016)

    Article  Google Scholar 

  27. Garg, H.: Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process. Comput. Math. Organ. Theory 23, 546–571 (2017)

    Article  Google Scholar 

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

    Article  Google Scholar 

  29. Zeng, S.: Pythagorean fuzzy multiattribute group decision making with probabilistic information and OWA approach. Int. J. Intell. Syst. 32, 1136–1150 (2017)

    Article  Google Scholar 

  30. Zeng, S., Cao, C., Deng, Y.: Pythagorean fuzzy information aggregation based on weighted induced operator and its application to \(R\)&\(D\) projections selection. Informatica 29(3), 567–580 (2018)

    Google Scholar 

  31. Peng, X.D., Yang, Y.: Some results for Pythagorean fuzzy sets. Int. J. Intell. Syst. 30, 1133–1160 (2015)

    Article  Google Scholar 

  32. Herrera-Viedma, E., Herrera, F., Chiclana, F., Luque, M.: some issues on consistency of fuzzy preference relations. Eur. J. Oper. Res. 154, 98–109 (2004)

    Article  MathSciNet  Google Scholar 

  33. Hu, Q., Yu, D., Guo, M.: Fuzzy preference based rough sets. Inf. Sci. 180, 2003–2022 (2010)

    Article  MathSciNet  Google Scholar 

  34. Pan, W., She, K., Wei, P.: Multi-granulation fuzzy preference relation rough set for ordinal decision system. Fuzzy Sets Syst. 312, 87–108 (2017)

    Article  MathSciNet  Google Scholar 

  35. Garg, H.: A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. Int. J. Intell. Syst. 1–35 (2011)

  36. Rahman, K., Abdullah, S., Ahmed, R., Ullah, U.: Pythagorean fuzzy Einstein weighted geometric aggregation operator and their application to multiple attribute group decision making. J. Intell. Fuzzy Syst. 33(1), 635–647 (2017)

    Article  Google Scholar 

  37. Rahman, K., Abdullah, S., Ali, A., Amin, F.: Pythagorean fuzzy Einstein hybrid averaging aggregation operator and its application to multiple-attribute group decision making. J. Intell. Syst. 29(1), 736–752 (2020)

    Article  Google Scholar 

  38. Wei, G., Garg, H., Gao, H., Wei, C.: Interval-valued Pythagorean fuzzy Maclaurin symmetric mean operators in multiple attribute decision making. IEEE Access 6(1), 67866–67884 (2018)

    Article  Google Scholar 

Download references

Acknowledgements

This research is supported by National Natural Science Foundation of China (Nos. 71771140 and 71471172), (Project of cultural masters and “the four kinds of a batch” talents), the Special Funds of Taishan Scholars Project of Shandong Province (No. ts201511045).

Author information

Authors and Affiliations

  1. School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, 250014, Shandong, China

    Peide Liu

  2. Department of Mathematics & Statistics, Riphah International University, Hajj Complex I-14, Islamabad, Pakistan

    Abbas Ali

  3. Department of Mathematics & Statistics, Bacha Khan University, Charsadda, Khyber Pakhtunkhwa, Pakistan

    Noor Rehman

  4. Department of Mathematics, Islamia College University, Peshawar, Khyber Pakhtunkhwa, Pakistan

    Syed Inayat Ali Shah

Authors
  1. Peide Liu
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Abbas Ali
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Noor Rehman
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Syed Inayat Ali Shah
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Noor Rehman.

Appendices

Appendices

1.1 Appendix 1

$$\begin{aligned} \mathcal {R}_{C\left( \mathcal {K}\right) }^{\uparrow }= & {} \left( \begin{array}{cccc} \left( 0.5000,0.5000\right) &{} \left( 0.4167,0.2500\right) &{} \left( 0.0417,0.0417\right) &{} \left( 0.0000,0.0000\right) \\ \left( 0.2500,0.4167\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.1250,0.2917\right) &{} \left( 0.0833,0.2500\right) \\ \left( 0.0417,0.0417\right) &{} \left( 0.2917,0.1250\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.4583,0.4583\right) \\ \left( 0.0000,0.0000\right) &{} \left( 0.2500,0.0833\right) &{} \left( 0.4583,0.4583\right) &{} \left( 0.5000,0.5000\right) \end{array} \right) . \end{aligned}$$

1.2 Appendix 2

$$\begin{aligned} {}_{A_{1}}\mathcal {R}^{1\downarrow }= & {} \left( \begin{array}{cccc} \left( 0.5000,0.5000\right) &{} \left( 0.0000,0.9000\right) &{} \left( 0.4000,0.6000\right) &{} \left( 0.3000,0.4000\right) \\ \left( 0.9000,0.0000\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.8000,0.1000\right) &{} \left( 0.8000,0.0000\right) \\ \left( 0.6000,0.4000\right) &{} \left( 0.1000,0.8000\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.4000,0.3000\right) \\ \left( 0.4000,0.3000\right) &{} \left( 0.0000,0.8000\right) &{} \left( 0.3000,0.4000\right) &{} \left( 0.5000,0.5000\right) \end{array} \right) \end{aligned}$$

1.3 Appendix 3

$$\begin{aligned} {}_{A_{2}}\mathcal {R}^{1\uparrow }= & {} \left( \begin{array}{cccc} \left( 0.5000,0.5000\right) &{} \left( 0.1000,0.7000\right) &{} \left( 0.4000,0.5000\right) &{} \left( 0.1000,0.6000\right) \\ \left( 0.7000,0.1000\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.7000,0.2000\right) &{} \left( 0.5000,0.4000\right) \\ \left( 0.5000,0.4000\right) &{} \left( 0.2000,0.7000\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.2000,0.4000\right) \\ \left( 0.6000,0.1000\right) &{} \left( 0.4000,0.5000\right) &{} \left( 0.6000,0.2000\right) &{} \left( 0.5000,0.5000\right) \end{array} \right) \end{aligned}$$

1.4 Appendix 4

$$\begin{aligned} {}_{A_{3}}\mathcal {R}^{1\downarrow }= & {} \left( \begin{array}{cccc} \left( 0.5000,0.5000\right) &{} \left( 0.3000,0.0000\right) &{} \left( 0.1000,0.0714\right) &{} \left( 0.3000,0.2143\right) \\ \left( 0.0000,0.8000\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.3000,0.5714\right) &{} \left( 0.2857,0.5000\right) \\ \left( 0.0714,0.6000\right) &{} \left( 0.5714,0.3000\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.3571,0.3000\right) \\ \left( 0.2000,0.7857\right) &{} \left( 0.5000,0.2857\right) &{} \left( 0.3000,0.3571\right) &{} \left( 0.5000,0.5000\right) \end{array} \right) \end{aligned}$$

1.5 Appendix 5

$$\begin{aligned} {}_{A_{4}}\mathcal {R}^{1\uparrow }= & {} \left( \begin{array}{cccc} \left( 0.5000,0.5000\right) &{} \left( 0.5000,0.4000\right) &{} \left( 0.4000,0.4000\right) &{} \left( 0.5000,0.2000\right) \\ \left( 0.4000,0.5000\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.3000,0.4000\right) &{} \left( 0.4000,0.2000\right) \\ \left( 0.4000,0.4000\right) &{} \left( 0.4000,0.3000\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.6000,0.3000\right) \\ \left( 0.2000,0.5000\right) &{} \left( 0.2000,0.4000\right) &{} \left( 0.3000,0.6000\right) &{} \left( 0.5000,0.5000\right) \end{array} \right) \end{aligned}$$

1.6 Appendix 6

$$\begin{aligned} {}_{A_{1}}\mathcal {R}^{2\downarrow }= & {} \left( \begin{array}{cccc} \left( 0.5000,0.5000\right) &{} \left( 0.8000,0.2000\right) &{} \left( 0.6000,0.3000\right) &{} \left( 0.8000,0.1000\right) \\ \left( 0.2000,0.8000\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.3000,0.6000\right) &{} \left( 0.5000,0.4000\right) \\ \left( 0.3000,0.6000\right) &{} \left( 0.6000,0.3000\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.7000,0.3000\right) \\ \left( 0.1000,0.2000\right) &{} \left( 0.4000,0.5000\right) &{} \left( 0.3000,0.3000\right) &{} \left( 0.5000,0.5000\right) \end{array} \right) \end{aligned}$$

1.7 Appendix 7

$$\begin{aligned} {}_{A_{2}}\mathcal {R}^{2\uparrow }= & {} \left( \begin{array}{cccc} \left( 0.5000,0.5000\right) &{} \left( 0.6000,0.3000\right) &{} \left( 0.4000,0.5000\right) &{} \left( 0.6000,0.3000\right) \\ \left( 0.3000,0.6000\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.2000,0.6000\right) &{} \left( 0.4000,0.4000\right) \\ \left( 0.5000,0.4000\right) &{} \left( 0.6000,0.2000\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.7000,0.3000\right) \\ \left( 0.3000,0.6000\right) &{} \left( 0.4000,0.4000\right) &{} \left( 0.3000,0.7000\right) &{} \left( 0.5000,0.5000\right) \end{array} \right) \end{aligned}$$

1.8 Appendix 8

$$\begin{aligned} {}_{A_{3}}\mathcal {R}^{2\downarrow }= & {} \left( \begin{array}{cccc} \left( 0.5000,0.5000\right) &{} \left( 0.0000,0.9000\right) &{} \left( 0.2000,0.8000\right) &{} \left( 0.3000,0.6000\right) \\ \left( 0.9000,0.0000\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.6000,0.3000\right) &{} \left( 0.8000,0.2000\right) \\ \left( 0.8000,0.2000\right) &{} \left( 0.3000,0.6000\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.6000,0.3000\right) \\ \left( 0.6000,0.3000\right) &{} \left( 0.2000,0.6000\right) &{} \left( 0.3000,0.6000\right) &{} \left( 0.5000,0.5000\right) \end{array} \right) \end{aligned}$$

1.9 Appendix 9

$$\begin{aligned} {}_{A_{4}}\mathcal {R}^{2\uparrow }= & {} \left( \begin{array}{cccc} \left( 0.5000,0.5000\right) &{} \left( 0.3000,0.6000\right) &{} \left( 0.7000,0.1000\right) &{} \left( 0.4000,0.4000\right) \\ \left( 0.6000,0.3000\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.9000,0.0000\right) &{} \left( 0.6000,0.3000\right) \\ \left( 0.1000,0.7000\right) &{} \left( 0.0000,0.9000\right) &{} \left( 0.5000,0.5000\right) &{} \left( 0.2000,0.8000\right) \\ \left( 0.4000,0.4000\right) &{} \left( 0.3000,0.6000\right) &{} \left( 0.8000,0.2000\right) &{} \left( 0.5000,0.5000\right) \end{array} \right) . \end{aligned}$$

1.10 Appendix 10

See Table 8.

Table 8 Different score functions
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, P., Ali, A., Rehman, N. et al. Another View on Intuitionistic Fuzzy Preference Relation-Based Aggregation Operators and Their Applications. Int. J. Fuzzy Syst. 22, 1786–1800 (2020). https://doi.org/10.1007/s40815-020-00882-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-020-00882-1

Keywords