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International Workshop Soft Computing Applications

SOFA 2018: Soft Computing Applications pp 276–288Cite as

Cubic Hesitant Fuzzy Heronian Mean Operators and Their Application in Multi Criteria Decision Making

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1222))

Abstract

This paper contains Heronian mean operators for cubic hesitant fuzzy sets. These operators include cubic hesitant fuzzy Heronian mean, cubic hesitant fuzzy geometric Heronian mean, cubic hesitant fuzzy weighted heronian mean, cubic hesitant fuzzy weighted geometric Heronian mean operators that help to aggregate the given information and show the association amongst given arguments. In the end, a multi criteria decision making problem has been solved through cubic hesitant fuzzy weighted geometric Heronian mean operators.

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References

  1. Ali, M.I., Feng, F., Liu, X., Min, W.K., Shabir, M.: On some new operations in soft set theory. Comput. Math. Appl. 57, 1547–1553 (2009)

    MathSciNet  MATH  Google Scholar 

  2. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 31, 87–96 (1986)

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  4. Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions a Guide for Practitioners. Springer, Berlin (2007)

    Google Scholar 

  5. Chakravarthi, M.K., Venkatesan, N.: Adaptive type-2 fuzzy controller for nonlinear delay dominant MIMO systems: an experimental paradigm in LabVIEW. Int. J. Adv. Intell. Parad. 10, 354–373 (2018)

    Google Scholar 

  6. Chen, N., Xu, Z.S., Xia, M.M.: Interval valued hesitant preference relations and their applications to group decision making. Knowl. Based Syst. 37, 528–540 (2013)

    Google Scholar 

  7. Chu, Y., Liu, P.: Some two-dimensional uncertain linguistic Heronian mean operators and their application in multiple attribute decision making. Neural Comput. Appl. 26, 1461–1480 (2015)

    Google Scholar 

  8. Fernandez, R.P., Alonso, P., Bustince, H., Diaz, I., Montes, S.: Applications of finite interval-valued hesitant fuzzy preference relations in group decision making. Inf. Sci. 326, 89–101 (2016)

    MathSciNet  MATH  Google Scholar 

  9. Hayat, K., Ali, M.I., Alcantud, J.C.R., Cao, B.Y., Tariq, K.U.: Best concept selection in design process: an application of generalized intuitionistic fuzzy soft sets. J. Intell. Fuzzy Syst. 35, 5707–5720 (2018)

    Google Scholar 

  10. Hong, D.H., Choi, C.H.: Multi criteria fuzzy decision making problems based on vague set theory. Fuzzy Sets Syst. 21, 1–17 (2000)

    Google Scholar 

  11. Hwang, C.L., Yoon, K.: Multiple Attribute Decision Making Methods and Application. Springer, New York (1981)

    MATH  Google Scholar 

  12. Jun, Y.B., Kim, C.S., Yang, K.O.: Cubic sets. Ann. Fuzzy Math. Inform. 4, 83–98 (2012)

    MathSciNet  MATH  Google Scholar 

  13. Karaaslan, F., Hayat, K.: Some new operations on single-valued neutrosophic matrices and their applications in multi-criteria group decision making. Appl. Intell. 48, 4594–4614 (2018)

    Google Scholar 

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

    MATH  Google Scholar 

  15. Li, Y., Liu, P.: Some Heronian mean operators with 2-tuple linguistic information and their application to multiple attribute group decision making. Technol. Econ. Dev. Econ. 21, 797–814 (2015)

    Google Scholar 

  16. Liu, P., Liu, Z., Zhang, X.: Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making. Appl. Math. Comput. 230, 570–586 (2014)

    MathSciNet  MATH  Google Scholar 

  17. Liu, P., Chen, S.M.: Group decision making based on Heronian aggregation operators of intuitionistic fuzzy numbers. IEEE Trans. Cybern. 47(9), 2514–2530 (2017)

    Google Scholar 

  18. Liu, P., Zhang, L.: Multiple criteria decision making method based on neutrosophic hesitant fuzzy Heronian mean aggregation operators. J. Intell. Fuzzy Syst. 32, 303–319 (2017)

    MATH  Google Scholar 

  19. Lu, Z., Ye, J.: Cosine measures of neutrosophic cubic sets for multiple attribute decision-making. Symmetry. 9(7), 121, 1–10 (2017)

    Google Scholar 

  20. Mahmood, T., Mehmood, F., Khan, Q.: Cubic Hesitant fuzzy sets and their applications to multi criteria decision making. Int. J. Algebra Stat. 5, 19–51 (2016)

    MATH  Google Scholar 

  21. Mahmood, T., Mehmood, F., Khan, Q.: Some generalized aggregation operators for cubic hesitant fuzzy sets and their applications to multi criteria decision making. Punjab Univ. J. Math. 49, 31–49 (2017)

    MathSciNet  MATH  Google Scholar 

  22. Nayagam, V.L.G., Muralikrish, S., Sivaraman, G.: Multi criteria decision making method based on interval valued intuitionistic fuzzy sets. Expert. Syst. Appl. 38, 1464–1467 (2011)

    Google Scholar 

  23. Sudha, V.K., Sudhakar, R., Balas, V.E.: Fuzzy rule-based segmentation of CT brain images of hemorrhage for compression. Int. J. Adv. Intell. Parad. 4, 256–267 (2014)

    Google Scholar 

  24. Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decision. In: The 18th IEEE International Conference on Fuzzy Systems, Korea, Jeju Island, pp. 1378–1382 (2009)

    Google Scholar 

  25. Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25, 529–539 (2010)

    MATH  Google Scholar 

  26. Viedma, H.E., Alonso, E., Chiclana, S., Herrera, F.: A consensus model for group decision making with incomplete fuzzy preference relations. IEEE Trans. Fuzzy Syst. 15, 863–877 (2007)

    MATH  Google Scholar 

  27. Xia, M.M., Xu, Z.S.: Hesitant fuzzy information aggregation in decision making. Int. J. Approx. Reason. 52, 395–407 (2011)

    MathSciNet  MATH  Google Scholar 

  28. Xia, M.M., Xu, Z.S., Chen, N.: Some hesitant fuzzy aggregation operators with their application in group decision making. Group Decis. Negot. 22, 259–279 (2013)

    Google Scholar 

  29. Xu, Z.S., Da, Q.L.: An overview of operators for aggregating information. Int. J. Intell. Syst. 18, 953–969 (2003)

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  32. Ye, J.: Linguistic neutrosophic cubic numbers and their multiple attribute decision-making method. Information. 8(3), 110, 1–11 (2017)

    Google Scholar 

  33. Ye, J.: Multiple attribute decision-making method based on linguistic cubic variables. J. Intell. Fuzzy Syst. (2018). https://doi.org/10.3233/JIFS-171413

    Article  MATH  Google Scholar 

  34. Yu, D., Wu, Y.: Interval valued intuitionistic fuzzy Heronian mean operators and their application in multi criteria decision making. Afr. J. Bus. Manag. 6, 4158 (2012)

    Google Scholar 

  35. Yu, D.: Intuitionistic fuzzy geometric Heronian mean aggregation operators. Appl. Soft Comput. 13, 1235–1246 (2013)

    Google Scholar 

  36. Yu, D.: Hesitant fuzzy multi criteria decision making methods based on Heronian mean. Technol. Econ. Dev. Econ., 1–20 (2015)

    Google Scholar 

  37. Yu, S.M., Zhou, H., Chen, X.H., Wang, J.Q.: A multi criteria decision making method based on Heronian mean operators under a linguistic hesitant fuzzy environment. Asia Pac. J. Oper. Res. 32, 1550035 (2015)

    MathSciNet  MATH  Google Scholar 

  38. Yordanova, S., Jain, L.C.: Design of supervisor-based adaptive process fuzzy logic control. Int. J. Adv. Intell. Parad. 9, 385–401 (2016)

    Google Scholar 

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

    MATH  Google Scholar 

  40. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-I. Inf. Sci. 8, 199–249 (1975)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Beijing Key Laboratory on MCAACI, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 102488, China

    Faisal Mehmood

  2. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, China

    Khizar Hayat

  3. Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000, Pakistan

    Tahir Mahmood

  4. Department of Computer Science and Technology, Guangzhou University, Guangzhou, 510006, China

    Muhammad Arif

Authors
  1. Faisal Mehmood
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  2. Khizar Hayat
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  3. Tahir Mahmood
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  4. Muhammad Arif
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Corresponding author

Correspondence to Faisal Mehmood .

Editor information

Editors and Affiliations

  1. "Aurel Vlaicu" University of Arad, Faculty of Engineering, Arad, Romania

    Valentina Emilia Balas

  2. Faculty of Engineering and Information Technology, University of Technology Sydney, Centre for Artificial Intelligence, Sydney, Australia

    Lakhmi C. Jain

  3. Faculty of Engineering, “Aurel Vlaicu” University of Arad, Arad, Arad, Romania

    Marius Mircea Balas

  4. Department of Information Technology and Programming, Azerbaijan Technical University, Baku, Azerbaijan

    Shahnaz N. Shahbazova

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Mehmood, F., Hayat, K., Mahmood, T., Arif, M. (2021). Cubic Hesitant Fuzzy Heronian Mean Operators and Their Application in Multi Criteria Decision Making. In: Balas, V., Jain, L., Balas, M., Shahbazova, S. (eds) Soft Computing Applications. SOFA 2018. Advances in Intelligent Systems and Computing, vol 1222. Springer, Cham. https://doi.org/10.1007/978-3-030-52190-5_20

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