Intuitionistic Fuzzy Soft Aggregation Operator Based on Einstein Norms and Its Applications in Decision-Making

  • Rishu AroraEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 940)


The manuscript aims to create a few aggregation operators based on Einstein norms under intuitionistic fuzzy (IF) soft set environment. For this, some operational laws based on Einstein sum and product are discussed. Then, based on these operations, Einstein averaging and geometric operators such as IF soft weighted Einstein averaging (IFSWEA) and IF soft weighted Einstein geometric (IFSWEG) operator are proposed. Further, some of their properties are investigated and the relationship between the proposed operators and the existing ones is explored. Furthermore, an approach for solving DM problems has been presented and illustrated with an example for demonstrating the effectiveness of proposed work.


Aggregation operator Einstein operator Intuitionistic fuzzy soft set Decision-making 



The author would like to thank the Department of Science & Technology, New Delhi, India for providing financial support under WOS-A scheme wide File No. SR/WOS-A/PM-77/2016 during the preparation of this manuscript.


  1. 1.
    Zadeh, L.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)CrossRefGoogle Scholar
  2. 2.
    Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Gau, W.L., Buehrer, D.J.: Vague sets. IEEE Trans. Syst. Man Cybern. 23(2), 610–614 (1993). Scholar
  4. 4.
    Atanassov, K., Gargov, G.: Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31(3), 343–349 (1989)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Molodtsov, D.: Soft set theory-first results. Comput. Math. Appl. 37(4–5), 19–31 (1999)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Maji, P.K., Biswas, R., Roy, A.R.: Fuzzy soft sets. J. Fuzzy Math. 9(3), 589–602 (2001)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Maji, P.K., Biswas, R., Roy, A.R.: Intuitionistic fuzzy soft sets. J. Fuzzy Math. 9(3), 677–692 (2001)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Bora, M., Neog, T.J., Sut, D.K.: Some new operations of intuitionistic fuzzy soft sets. Int. J. Soft Comput. Eng. 2(4), 2231–2307 (2012)Google Scholar
  9. 9.
    Jiang, Y., Tang, Y., Liu, H., Chen, Z.: Entropy on intuitionistic fuzzy soft sets and on interval-valued fuzzy soft sets. Inf. Sci. 240, 95–114 (2013)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Selvachandran, G., Maji, P., Faisal, R.Q., Salleh, A.R.: Distance and distance induced intuitionistic entropy of generalized intuitionistic fuzzy soft sets. Appl. Intell. 47, 132–147 (2017)CrossRefGoogle Scholar
  11. 11.
    Sarala, N., Suganya, B.: An application of similarity measure of intuitionistic fuzzy soft set based on distance in medical diagnosis. Int. J. Sci. Res. 4, 2298–2303 (2016)Google Scholar
  12. 12.
    Muthukumar, P., Krishnan, G.S.S.: A similarity measure of intuitionistic fuzzy soft sets and its application in medical diagnosis. Appl. Soft Comput. 41, 148–156 (2016)CrossRefGoogle Scholar
  13. 13.
    Khalid, A., Abbas, M.: Distance measures and operations in intuitionistic and interval-valued intuitionistic fuzzy soft set theory. Int. J. Fuzzy Syst. 17(3), 490–497 (2015)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Arora, R., Garg, H.: A robust aggregation operators for multi criteria decision making with intuitionistic fuzzy soft set environment. Scientica Iranica 25(2), 931–942 (2018)Google Scholar
  15. 15.
    Arora, R., Garg, H.: Prioritized averaging/geometric aggregation operators under the intuitionistic fuzzy soft set environment. Scientica Iranica 25(1), 466–482 (2018)Google Scholar
  16. 16.
    Garg, H., Arora, R.: Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decision-making. Appl. Intell. 48(2), 343–356 (2018)CrossRefGoogle Scholar
  17. 17.
    Garg, H., Arora, R.: Bonferroni mean aggregation operators under intuitionistic fuzzy soft set environment and their applications to decision-making. J. Oper. Res. Soc. 1–14 (2018).

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

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

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