Affiliations: [a] Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan
| [b] Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan
| [c] Department of Electronics Engineering, University of Engineering and Technology, Taxila sub campus Chakwal, Pakistan
Correspondence:
[*]
Corresponding author. Saleem Abdullah, Department of Mathematics, Abdul Wali Khan University, 23200 Mardan, Pakistan. E-mail: saleemabdullah@awkum.edu.pk.
Abstract: The key objective of the present proposed work in this paper is introduced a new version of picture fuzzy set so called spherical fuzzy sets (SFS). spherical fuzzy set is a new extension of picture fuzzy sets and Pythagorean fuzzy sets. In spherical fuzzy sets, membership degrees are gratifying the condition 0 ⩽ P2 (x) + I2 (x) + N2 (x) ⩽1 instead of 0 ⩽ P (x) + I (x) + N (x) ⩽1 as is in picture fuzzy sets. In this paper, we investigate the basic operations of spherical fuzzy sets and discuss some related results. We extend operational laws to aggregation operators and introduce weighted averaging and weighted geometric aggregation operators based on spherical fuzzy number’s. Further a multi attribute decision making method is developed and these aggregation operators are utilized. Finally, we constructed a numerical approach for implementation of proposed technique.
Keywords: Spherical fuzzy sets, aggregation operators, multi-attribute decision making problem
