Analyzing risk factors of tuberculosis using type-2 interval-valued trapezoidal fuzzy numbers with Einstein aggregation operators extended to MCDM.

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.