Qiyas Muhammad, Abdullah Saleem, Khan Saifullah, Naeem Muhammad
Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan.
Department of Preparatory Year, Umm Al-Qura University, Makkah, Saudi Arabia.
Granul Comput. 2022;7(1):141-162. doi: 10.1007/s41066-021-00256-4. Epub 2021 Mar 22.
Spherical fuzzy set (SFS) is also one of the fundamental concepts for address more uncertainties in decision problems than the existing structures of fuzzy sets, and thus its implementation was more substantial. The well-known sine trigonometric function maintains the periodicity and symmetry of the origin in nature and thus satisfies the expectations of the experts over the multi parameters. Taking this feature and the significance of the SFSs into the consideration, the main objective of the article is to describe some reliable sine trigonometric laws for SFSs. Associated with these laws, we develop new average and geometric aggregation operators to aggregate the Spherical fuzzy numbers. Then, we presented a group decision-making strategy to address the multi-attribute group decision-making problem using the developed aggregation operators. To verify the value of the defined operators, a MAGDM strategy is provided along with an application for the selection of an authentic COVID-19 laboratory. Moreover, a comparative study is also performed to present the effectiveness of the developed approach.
球形模糊集(SFS)也是一个基本概念,用于解决决策问题中比现有模糊集结构更多的不确定性,因此其实现更为重要。著名的正弦三角函数在本质上保持了原点的周期性和对称性,从而满足了专家对多参数的期望。考虑到这一特性以及球形模糊集的重要性,本文的主要目的是描述一些适用于球形模糊集的可靠正弦三角定律。与这些定律相关联,我们开发了新的均值和几何聚合算子来聚合球形模糊数。然后,我们提出了一种群体决策策略,使用所开发的聚合算子来解决多属性群体决策问题。为了验证所定义算子的价值,提供了一种多属性群体决策策略以及一个用于选择正宗COVID-19实验室的应用。此外,还进行了一项比较研究,以展示所开发方法的有效性。