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Some Picture Fuzzy Aggregation Operators and Their Applications to Multicriteria Decision-Making

  • Research Article - Systems Engineering
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Abstract

The objective of the work is to present some series of the aggregation operators for the picture fuzzy sets (PFSs). As PFSs have been an extended version of the intuitionistic fuzzy set theory which not only considers the degree of acceptance or rejection but also taken into the account the degree of refusal during the analysis. Thus, by considering all these degrees, some aggregation operators, namely picture fuzzy weighted average, picture fuzzy ordered weighted average, and picture fuzzy hybrid average aggregation operators, have been proposed along with their desirable properties. A decision-making approach based on these operators has also been presented. Finally, an illustrative example has been given for demonstrating the approach.

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References

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

    Article  MATH  Google Scholar 

  2. Atanassov, K.; Gargov, G.: Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31, 343–349 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  3. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MATH  Google Scholar 

  4. Du, Y.; Liu, P.: Extended fuzzy VIKOR method with intuitionistic trapezoidal fuzzy numbers. Inf. Int. Interdiscip. J. 14(8), 2575–2583 (2011)

    MATH  MathSciNet  Google Scholar 

  5. Garg, H.: 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 (2016)

    Article  Google Scholar 

  6. 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 

  7. Garg, H.: A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making processes. Int. J. Intell. Syst. 31(12), 1234–1252 (2016)

    Article  Google Scholar 

  8. Garg, H.: Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application. Eng. Appl. Artif. Intell. 60, 164–174 (2017)

    Article  Google Scholar 

  9. Garg, H.; Agarwal, N.; Tripathi, A.: Generalized intuitionistic fuzzy entropy measure of order \(\alpha \) and degree \(\beta \) and its applications to multi-criteria decision making problem. Int. J. Fuzzy Syst. Appl. 6(1), 86–107 (2017)

    Article  Google Scholar 

  10. Kumar, K.; Garg, H.: TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment. Comput. Appl. Math. (2016). doi:10.1007/s40314-016-0402-0

    Google Scholar 

  11. Liu, P.: Multi-attribute decision making method research based on interval vague set and TOPSIS method. Technol. Econ. Dev. Econ. 15(3), 453–463 (2009)

    Article  Google Scholar 

  12. Lourenzuttia, R.; Krohlingb, R.A.: A study of TODIM in a intuitionistic fuzzy and random environment. Expert Syst. Appl. 40(16), 6459–6468 (2013)

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. Yager, R.R.: On ordered weighted avergaing aggregation operators in multi-criteria decision making. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)

    Article  Google Scholar 

  15. Yager, R.R.; Kacprzyk, J.: The Ordered Weighted Averaging Operators: Theory and Applications. M.A., Kluwer, Boston (1997)

    Book  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  17. Wang, W.; Liu, X.: Intuitionistic fuzzy information aggregation using einstein operations. IEEE Trans. Fuzzy Syst. 20(5), 923–938 (2012)

    Article  Google Scholar 

  18. Garg, H.: A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems. Appl. Soft Comput. 38, 988–999 (2016). doi:10.1016/j.asoc.2015.10.040

    Article  Google Scholar 

  19. Garg, H.: Some series of intuitionistic fuzzy interactive averaging aggregation operators. SpringerPlus 5(1), 999 (2016). doi:10.1186/s40064-016-2591-9

    Article  Google Scholar 

  20. Xu, Y.; Wang, H.; Merigo, J.M.: Intuitionistic fuzzy einstein choquet intergral operators for multiple attribute decision making. Technol. Econ. Dev. Econ. 20(2), 227–253 (2014)

    Article  Google Scholar 

  21. Wan, S.P.; Xu, G.L.; Wang, F.; Dong, J.Y.: A new method for atanassov’s interval-valued intuitionistic fuzzy magdm with incomplete attribute weight information. Inf. Sci. 316, 329–347 (2015)

    Article  Google Scholar 

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

    Article  Google Scholar 

  23. Garg, H.: Generalized Pythagorean fuzzy geometric aggregation operators using einstein t-norm and t-conorm for multicriteria decision-making process. Int. J. Intell. Syst. (2016). doi:10.1002/int.21860

  24. Garg, H.: Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process. Comput. Math. Organ. Theory (2017). doi:10.1007/s10588-017-9242-8

  25. Zavadskas, E.K.; Antucheviciene, J.; Hajiagha, S.H.R.; Hashemi, S.S.: Extension of weighted aggregated sum product assessment with interval-valued intuitionistic fuzzy numbers (WASPAS-IVIF). Appl. Soft Comput. 24, 1013–1021 (2014)

    Article  Google Scholar 

  26. Hwang, C.L.; Yoon, K.: Multiple Attribute Decision Making Methods and Applications A State-of-the-Art Survey. Springer, Berlin (1981)

    Book  MATH  Google Scholar 

  27. Cuong, B.C.: Picture fuzzy sets -first results. part 1, seminar neuro-fuzzy systems with applications. Tech. rep., Instiute of Mathematics, Hanoi (2013)

  28. Cuong, B.C.: Picture fuzzy sets -first results. part 2, seminar neuro-fuzzy systems with applications. Tech. rep., Instiute of Mathematics, Hanoi (2013)

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

    MATH  MathSciNet  Google Scholar 

  30. Son, L.H.: Generalized picture distance measure and applications to picture fuzzy clustering. Appl. Soft Comput. 46, 284–295 (2016)

    Article  Google Scholar 

  31. Wei, G.W.: Picture fuzzy cross-entropy for multiple attribute decision making problems. J. Bus. Econ. Manag. 17(4), 491–502 (2016)

    Article  Google Scholar 

  32. Klir, G.J.; Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall of India Private Limited, New Delhi (2005)

    MATH  Google Scholar 

  33. Wang, X.; Triantaphyllou, E.: Ranking irregularities when evaluating alternatives by using some ELECTRE methods. Omega Int. J. Manag. Sci. 36, 45–63 (2008)

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics, Thapar University Patiala, Patiala, Punjab, 147004, India

    Harish Garg

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  1. Harish Garg
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Correspondence to Harish Garg.

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Garg, H. Some Picture Fuzzy Aggregation Operators and Their Applications to Multicriteria Decision-Making. Arab J Sci Eng 42, 5275–5290 (2017). https://doi.org/10.1007/s13369-017-2625-9

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