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Solid Waste Collection System Selection Based on Sine Trigonometric Spherical Hesitant Fuzzy Aggregation Information

Muhammad Naeem1, Aziz Khan2, Saleem Abdullah2,*, Shahzaib Ashraf3, Ahmad Ali Ahmad Khammash4

1 Deanship of Combined First Year, Umm Al-Qura University, Makkah, Saudi Arabia
2 Department of Mathematics, Abdul Wali Khan University, Mardan, 23200, Pakistan
3 Department of Mathematics and Statistics, Bacha Khan University, Charsadda, 24420, Pakistan
4 Department of Mathematics, Deanship of Applied Sciences, Umm Al-Qura University, Makkah, Saudi Arabia

* Corresponding Author: Saleem Abdullah. Email:

Intelligent Automation & Soft Computing 2021, 28(2), 459-476.


Spherical fuzzy set (SFS) as one of several non-standard fuzzy sets, it introduces a number triplet (a,b,c) that satisfies the requirement a2 + b2 + c2 ≤ 1 to express membership grades. Due to the expression, SFS has a more extensive description space when describing fuzzy information, which attracts more attention in scientific research and engineering practice. Just for this reason, how to describe the fuzzy information more reasonably and perfectly is the hot that scholars pay close attention to. In view of this hot, in this paper, the notion of spherical hesitant fuzzy set is introduced as a generalization of spherical fuzzy sets. Some basic operations using sine trigonometric function are presented for spherical hesitant fuzzy sets. We define spherical hesitant fuzzy weighted average and spherical hesitant fuzzy weighted geometric aggregation operators. Based on these new aggregation operators, we propose a method for multi-criteria decision making (MCDM) in the spherical hesitant fuzzy information. Besides, a numerical real-life application about solid waste collection system selection is provided to demonstrate the validity of the proposed approaches along with relevant discussions, the merits of proposed approaches are also analyzed by validity test.


Cite This Article

M. Naeem, A. Khan, S. Abdullah, S. Ashraf and A. Ali Ahmad Khammash, "Solid waste collection system selection based on sine trigonometric spherical hesitant fuzzy aggregation information," Intelligent Automation & Soft Computing, vol. 28, no.2, pp. 459–476, 2021.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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