Interval-valued intuitionistic fuzzy AROMAN method and its application in sustainable wastewater treatment technology selection

In the theory of interval-valued intuitionistic fuzzy set (IVIFS), the rating/grade of an element is the subset of the closed interval [0, 1], therefore the IVIFS doctrine is more useful for the decision expert to present their judgments in terms of intervals rather than the crisp values. The present work develops an integrated decision-making methodology for evaluating sustainable wastewater treatment technologies within the context of IVIFS. The proposed decision-making framework is divided into three stages. First, some Yager weighted aggregation operators and their axioms are developed to combine the interval-valued intuitionistic fuzzy information. These operators can offer us a flexible way to solve the realistic multi-criteria decision-making problems under IVIFS context. Second, an extension of Symmetry Point of Criterion model is introduced to determine the criteria weights under IVIFS environment. Third, an integrated alternative ranking order model accounting for two-step normalization (AROMAN) approach is proposed from IVIF information perspective. Next, the practicability and efficacy of the developed model is proven by implementing it on a case study of sustainable wastewater treatment technologies evaluation problem with multiple criteria and decision experts. Finally, comparative analysis is discussed to illustrate the consistency and robustness of the obtained outcomes.