Sheela Rani M, Dhanasekar S
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, 600127, India.
Heliyon. 2024 Aug 12;10(16):e35997. doi: 10.1016/j.heliyon.2024.e35997. eCollection 2024 Aug 30.
The principal motive of this work is to evolve and initiate an extension from interval-valued fuzzy sets to type-2 interval-valued fuzzy sets (T2IVFS) related to weighted aggregation functions containing the Einstein operator. The chief reason for this extension is that the constancy of the terms can also be taken into data during the aggregation operation. The main goal of this article is to compose the aggregation operators and their characteristics such as the Type-2 interval-valued fuzzy Einstein weighted arithmetic aggregating operator (T2IVFEWA), Type-2 interval-valued fuzzy Einstein weighted geometric aggregating operator (T2IVFEWG), and the characteristics are expressed. At last, to intimate the effectiveness of the suggested approach and explicate the purpose of these operators, a hybrid multi-criteria decision-making problem (MCDM) to select the best risk factor for Tuberculosis (TB) is considered and the result is compared with the outcome of the existing operators and methods. Additionally, a sensitivity analysis was conducted to verify the robustness of the proposed decision-making process.
这项工作的主要动机是发展并启动从区间值模糊集到与包含爱因斯坦算子的加权聚合函数相关的二型区间值模糊集（T2IVFS）的扩展。进行这种扩展的主要原因是在聚合操作期间，项的常量也可以纳入数据。本文的主要目标是构建聚合算子及其特性，如二型区间值模糊爱因斯坦加权算术聚合算子（T2IVFEWA）、二型区间值模糊爱因斯坦加权几何聚合算子（T2IVFEWG），并阐述其特性。最后，为了说明所提方法的有效性并解释这些算子的用途，考虑了一个用于选择结核病（TB）最佳风险因素的混合多准则决策问题（MCDM），并将结果与现有算子和方法的结果进行比较。此外，还进行了敏感性分析以验证所提决策过程的稳健性。
