Research Article

The Application of GRA Method Base on Choquet Integral Using Spherical Fuzzy Information in Decision Making Problems

Number: 28 May 7, 2019
Shahzaib Ashraf *, Saleem Abdullah , Muhammad Qiyas , Aziz Khan
EN

The Application of GRA Method Base on Choquet Integral Using Spherical Fuzzy Information in Decision Making Problems

Abstract

Spherical fuzzy set is the generalized structure over existing structures of fuzzy sets to deals with uncertainty and imprecise information in decision-making problems. Viewing the effectiveness of the spherical fuzzy set, we developed a decision-making algorithm to deal with multi-criteria decision-making problems. In this paper, we extend operational laws to propose spherical fuzzy Choquet integral weighted averaging (SFCIWA) operator based on spherical fuzzy numbers. Further, the proposed SFCIWA operator is applied to multi-attribute group decision-making problems. Also, we propose the GRA method to aggregate the spherical fuzzy information. To implement the proposed models, we provide some numerical applications of group decision-making problems. Also compared with the previous model, we conclude that the proposed technique is more effective and reliable.

Keywords

Choquet integral,Spherical fuzzy Choquet integral weighted averaging (SFCIWA) operator,GRA method,Spherical fuzzy sets,Decision making technique.

Thanks

no funding supporting agency

References

  1. Ashraf, S. and Abdullah, S., 2019. Spherical aggregation operators and their application in multi-attribute group decision-making. International Journal of Intelligent Systems, 34(3), pp.493-523.
APA
Ashraf, S., Abdullah, S., Qiyas, M., & Khan, A. (2019). The Application of GRA Method Base on Choquet Integral Using Spherical Fuzzy Information in Decision Making Problems. Journal of New Theory, 28, 84-97. https://izlik.org/JA54KU94EK
AMA
1.Ashraf S, Abdullah S, Qiyas M, Khan A. The Application of GRA Method Base on Choquet Integral Using Spherical Fuzzy Information in Decision Making Problems. JNT. 2019;(28):84-97. https://izlik.org/JA54KU94EK
Chicago
Ashraf, Shahzaib, Saleem Abdullah, Muhammad Qiyas, and Aziz Khan. 2019. “The Application of GRA Method Base on Choquet Integral Using Spherical Fuzzy Information in Decision Making Problems”. Journal of New Theory, nos. 28: 84-97. https://izlik.org/JA54KU94EK.
EndNote
Ashraf S, Abdullah S, Qiyas M, Khan A (May 1, 2019) The Application of GRA Method Base on Choquet Integral Using Spherical Fuzzy Information in Decision Making Problems. Journal of New Theory 28 84–97.
IEEE
[1]S. Ashraf, S. Abdullah, M. Qiyas, and A. Khan, “The Application of GRA Method Base on Choquet Integral Using Spherical Fuzzy Information in Decision Making Problems”, JNT, no. 28, pp. 84–97, May 2019, [Online]. Available: https://izlik.org/JA54KU94EK
ISNAD
Ashraf, Shahzaib - Abdullah, Saleem - Qiyas, Muhammad - Khan, Aziz. “The Application of GRA Method Base on Choquet Integral Using Spherical Fuzzy Information in Decision Making Problems”. Journal of New Theory. 28 (May 1, 2019): 84-97. https://izlik.org/JA54KU94EK.
JAMA
1.Ashraf S, Abdullah S, Qiyas M, Khan A. The Application of GRA Method Base on Choquet Integral Using Spherical Fuzzy Information in Decision Making Problems. JNT. 2019;:84–97.
MLA
Ashraf, Shahzaib, et al. “The Application of GRA Method Base on Choquet Integral Using Spherical Fuzzy Information in Decision Making Problems”. Journal of New Theory, no. 28, May 2019, pp. 84-97, https://izlik.org/JA54KU94EK.
Vancouver
1.Shahzaib Ashraf, Saleem Abdullah, Muhammad Qiyas, Aziz Khan. The Application of GRA Method Base on Choquet Integral Using Spherical Fuzzy Information in Decision Making Problems. JNT [Internet]. 2019 May 1;(28):84-97. Available from: https://izlik.org/JA54KU94EK