Advertisement

Neutrality operations-based Pythagorean fuzzy aggregation operators and its applications to multiple attribute group decision-making process

  • Harish GargEmail author
Original Research

Abstract

Pythagorean fuzzy sets accommodate more uncertainties than the intuitionistic fuzzy sets and hence it is one of the most important concepts to describe the fuzzy information in the process of decision making. Under this environment, the main objective of the work is to develop some new operational laws and their corresponding weighted aggregation operators. For it, we define some new neutral addition and scalar multiplication operational laws by incorporating the features of a neutral character towards the membership degrees of the set and the probability sum. Some properties of the proposed laws are investigated. Then, associated with these operational laws, we define some novel Pythagorean fuzzy weighted, ordered weighted and hybrid neutral averaging aggregation operators for Pythagorean fuzzy information, which can neutrally treat the membership and non-membership degrees. The various relations and the characteristics of the proposed operators are discussed. Further, in order to ease with the possible application, we present an algorithm to solve the multiple attribute group decision-making problems under the Pythagorean fuzzy environment. Finally, a practical example is provided to illustrate the approach and show its superiority, advantages by comparing their performance with some several existing approaches.

Keywords

Pythagorean fuzzy sets Neutrality operations Aggregation operators Multi attribute group decision making 

Notes

References

  1. Arora R, Garg H (2018) A robust correlation coefficient measure of dual hesistant fuzzy soft sets and their application in decision making. Eng Appl Artif Intell 72:80–92CrossRefGoogle Scholar
  2. Arora R, Garg H (2019) Group decision-making method based on prioritized linguistic intuitionistic fuzzy aggregation operators and its fundamental properties. Comput Appl Math 38(2):1–36MathSciNetzbMATHCrossRefGoogle Scholar
  3. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96zbMATHCrossRefGoogle Scholar
  4. Chen SM, Chang CH (2016) Fuzzy multiattribute decision making based on transformation techniques of intuitionistic fuzzy values and intuitionistic fuzzy geometric averaging operators. Inf Sci 352–353:133–149zbMATHCrossRefGoogle Scholar
  5. Chen TY (2019) Multiple criteria decision analysis under complex uncertainty: a pearson-like correlation-based Pythagorean fuzzy compromise approach. Int J Intell Syst 34(1):114–151CrossRefGoogle Scholar
  6. Gao H (2018) Pythagorean fuzzy hamacher prioritized aggregation operators in multiple attribute decision making. J Intell Fuzzy Syst 35(2):2229–2245CrossRefGoogle Scholar
  7. Gao H, Lu M, Wei G, Wei Y (2018) Some novel pythagorean fuzzy interaction aggregation operators in multiple attribute decision making. Fundam Inf 159(4):385–428MathSciNetzbMATHCrossRefGoogle Scholar
  8. Garg H (2016a) Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making. Comput Ind Eng 101:53–69CrossRefGoogle Scholar
  9. Garg H (2016b) A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. Int J Intell Syst 31(9):886–920CrossRefGoogle Scholar
  10. Garg H (2016c) A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making processes. Int J Intell Syst 31(12):1234–1252CrossRefGoogle Scholar
  11. Garg H (2017a) Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process. Comput Math Organ Theory 23(4):546–571CrossRefGoogle Scholar
  12. Garg H (2017b) Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process. Int J Intell Syst 32(6):597–630CrossRefGoogle Scholar
  13. Garg H (2017c) Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application. Eng Appl Artif Intell 60:164–174CrossRefGoogle Scholar
  14. Garg H (2018a) Generalized Pythagorean fuzzy geometric interactive aggregation operators using Einstein operations and their application to decision making. J Exp Theor Artif Intell 30(6):763–794CrossRefGoogle Scholar
  15. Garg H (2018b) Hesitant Pythagorean fuzzy sets and their aggregation operators in multiple attribute decision making. Int J Uncertain Quantif 8(3):267–289MathSciNetCrossRefGoogle Scholar
  16. Garg H (2018c) Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision-making process. Int J Intell Syst 33(6):1234–1263CrossRefGoogle Scholar
  17. Garg H (2018d) New exponential operational laws and their aggregation operators for interval-valued Pythagorean fuzzy multicriteria decision-making. Int J Intell Syst 33(3):653–683CrossRefGoogle Scholar
  18. Garg H (2019a) Intuitionistic fuzzy hamacher aggregation operators with entropy weight and their applications to multi-criteria decision-making problems. Iran J Sci Technol Trans Electr Eng 43(3):597–613CrossRefGoogle Scholar
  19. Garg H (2019b) New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications. Int J Intell Syst 34(1):82–106CrossRefGoogle Scholar
  20. Garg H (2019c) Novel neutrality operation-based Pythagorean fuzzy geometric aggregation operators for multiple attribute group decision analysis. Int J Intell Syst 34(10):2459–2489CrossRefGoogle Scholar
  21. Garg H, Arora R (2019) Generalized intuitionistic fuzzy soft power aggregation operator based on t-norm and their application in multi criteria decision-making. Int J Intell Syst 34(2):215–246CrossRefGoogle Scholar
  22. Garg H, Kumar K (2019) Linguistic interval-valued atanassov intuitionistic fuzzy sets and their applications to group decision-making problems. In: IEEE Transactions on Fuzzy Systems, pp 1–10.  https://doi.org/10.1109/TFUZZ.2019.2897961
  23. Garg H, Nancy (2019) Linguistic single-valued neutrosophic power aggregation operators and their applications to group decision-making problems. IEEE/CAA Journal of Automatic Sinica pp 1 – 13,  https://doi.org/10.1109/JAS.2019.1911522
  24. Huang JY (2014) Intuitionistic fuzzy Hamacher aggregation operator and their application to multiple attribute decision making. J Intell Fuzzy Syst 27:505–513MathSciNetzbMATHGoogle Scholar
  25. Jana C, Pal M, Jq Wang (2019) Bipolar fuzzy dombi aggregation operators and its application in multiple-attribute decision-making process. J Ambient Intell Humaniz Comput 10(9):3533–3549CrossRefGoogle Scholar
  26. Kaur G, Garg H (2018) Cubic intuitionistic fuzzy aggregation operators. Int J Uncertain Quantif 8(5):405–427MathSciNetCrossRefGoogle Scholar
  27. Kaur G, Garg H (2019) Generalized cubic intuitionistic fuzzy aggregation operators using t-norm operations and their applications to group decision-making process. Arab J Sci Eng 44(3):2775–2794CrossRefGoogle Scholar
  28. Khan MSA, Abdullah S, Ali A, Amin F, Hussain F (2019) Pythagorean hesitant fuzzy choquet integral aggregation operators and their application to multi-attribute decision-making. Soft Comput 23(1):251–267zbMATHCrossRefGoogle Scholar
  29. Klir GJ, Yuan B (2005) Fuzzy sets and fuzzy logic: theory and applications. Prentice Hall of India Private Limited, New DelhizbMATHGoogle Scholar
  30. Liang D, Xu Z (2017) The new extension of topsis method for multiple criteria decision making with hesitant Pythagorean fuzzy sets. Appl Soft Comput 60:167–179CrossRefGoogle Scholar
  31. Liu P (2017) Some frank aggregation operators for interval-valued intuitionistic fuzzy numbers and their application to group decision making. J Mult Valued Log Soft Comput 29(1–2):183–223MathSciNetzbMATHGoogle Scholar
  32. Ma ZM, Xu ZS (2016) Symmetric Pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems. Int J Intell Syst 31(12):1198–1219CrossRefGoogle Scholar
  33. Nancy Garg H (2019) A novel divergence measure and its based TOPSIS method for multi criteria decision-making under single-valued neutrosophic environment. J Intell Fuzzy Syst 36(1):101–115CrossRefGoogle Scholar
  34. Nie RX, Tian ZP, Wang JQ, Hu JH (2019) Pythagorean fuzzy multiple criteria decision analysis based on shapley fuzzy measures and partitioned normalized weighted bonferroni mean operator. Int J Intell Syst 34(2):297–324CrossRefGoogle Scholar
  35. Peng X, Yang Y (2015) Some results for Pythagorean fuzzy sets. Int J Intell Syst 30(11):1133–1160MathSciNetCrossRefGoogle Scholar
  36. Peng X, Dai J, 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):2255–2282CrossRefGoogle Scholar
  37. Peng XD, Garg H (2018) Algorithms for interval-valued fuzzy soft sets in emergency decision making based on WDBA and CODAS with new information measure. Comput Ind Eng 119:439–452CrossRefGoogle Scholar
  38. Rani D, Garg H (2017) Distance measures between the complex intuitionistic fuzzy sets and its applications to the decision-making process. Int J Uncertain Quantif 7(5):423–439MathSciNetCrossRefGoogle Scholar
  39. Rani D, Garg H (2018) Complex intuitionistic fuzzy power aggregation operators and their applications in multi-criteria decision-making. Expert Syst 35(6):e12325.  https://doi.org/10.1111/exsy.12325 CrossRefGoogle Scholar
  40. Viriyasitavat W (2016) Multi-criteria selection for services selection in service workflow. J Ind Inf Integr 1:20–25Google Scholar
  41. Wang X, Triantaphyllou E (2008) Ranking irregularities when evaluating alternatives by using some ELECTRE methods. Omega Int J Manag Sci 36:45–63CrossRefGoogle Scholar
  42. Wei G, Zhao X, Wang H, Lin R (2013) Fuzzy power aggregation operators and their application to multiple attribute group decision making. Technol Econ Dev Econ 19(3):377–396CrossRefGoogle Scholar
  43. Wei GW, Lu M (2018) Pythagorean fuzzy power aggregation operators in multiple attribute decision maig. Int J Intell Syst 33(1):169–186MathSciNetCrossRefGoogle Scholar
  44. Xu LD (1988) A fuzzy multiobjective programming algorithm in decision support systems. Ann Oper Res 12(1):315–320MathSciNetCrossRefGoogle Scholar
  45. Xu ZS (2005) An overview of methods for determining owa weights. Int J Intell Syst 20:843–865zbMATHCrossRefGoogle Scholar
  46. Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187CrossRefGoogle Scholar
  47. Xu ZS, Hu H (2010) Projection models for intuitionistic fuzzy multiple attribute decision making. Int J Inf Technol Decis Mak 9:267–280zbMATHCrossRefGoogle Scholar
  48. Yager RR (1988) On ordered weighted avergaing aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern 18(1):183–190CrossRefGoogle Scholar
  49. Yager RR (2013) Pythagorean fuzzy subsets. Procedings joint IFSA world congress and NAFIPS annual meeting. Edmonton, Canada, pp 57–61CrossRefGoogle Scholar
  50. Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965CrossRefGoogle Scholar
  51. Yager RR, Abbasov AM (2013) Pythagorean membeship grades, complex numbers and decision making. Int J Intell Syst 28:436–452CrossRefGoogle Scholar
  52. Ye J (2017) Intuitionistic fuzzy hybrid arithmetic and geometric aggregation operators for the decision-making of mechanical design schemes. Appl Intell 47:743–751CrossRefGoogle Scholar
  53. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353zbMATHCrossRefGoogle Scholar
  54. Zeng S, Chen J, Li X (2016) A hybrid method for Pythagorean fuzzy multiple-criteria decision making. Int J Inf Technol Decis Mak 15(2):403–422CrossRefGoogle Scholar
  55. Zeng S, Mu Z, Baležentis T (2018) A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making. Int J Intell Syst 33(3):573–585CrossRefGoogle Scholar
  56. Zhang X (2016a) Multicriteria Pythagorean fuzzy decision analysis: a hierarchical QUALIFLEX approach with the closeness index-based ranking. Inf Sci 330:104–124CrossRefGoogle Scholar
  57. Zhang XL (2016b) A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. Int J Intell Syst 31:593–611CrossRefGoogle Scholar
  58. Zhang XL, Xu ZS (2014) Extension of TOPSIS to multi-criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29(12):1061–1078MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of MathematicsThapar Institute of Engineering and Technology (Deemed University)PatialaIndia

Personalised recommendations