Prioritizing Ventilator Machines in Emergency Scenarios Using Multi-Criteria Decision-Making with Circular Intuitionistic Fuzzy Set and Dombi Operations

In the modern age, the circular intuitionistic fuzzy (IF) set (CIFS) is highly popular because it includes a membership grade and a non-membership grade within the range of the unit interval [0,1], as well as a circular degree within the range of [0,√2]. In contrast, a simple IFS is based only on membership and non-membership grades within the range of [0,1]. Moreover, the theory of IFS is unable to handle information in which a circular degree is involved. Hence, the CIFS is the most generalized format of IFS. In decision-making (DM) sciences, multi-criteria decision making (MCDM) is one of the most effective approaches for combining data and opinions from different sources. It evaluates and selects the best option when a decision involves several criteria. The Dombi t-norm (DTNM) and Dombi t-conorm (DTCNM) are crucial tools for aggregating uncertain and imprecise information. The notion of a power aggregation operator (PAO) is also a powerful concept for evaluating the weight vectors (WV) of alternatives by combining them and their attributes. The idea of PAO is considered a valuable tool for the evaluation of WV, providing reliability in aggregated outcomes. Using the concepts of CIFS, PAOs, DTNM, and DTCNM operations, we construct a new family of aggregation operators (AOs) called circular IF Dombi power weighted averaging (CIFDPWA) and circular IF Dombi power weighted geometric (CIFDPWG) operators for finding reliable solutions to MCDM problems. We investigate some fundamental axioms of AOs, such as monotonicity, boundedness, and idempotency. We provide an MCDM algorithm based on the proposed theory. The case study details the best ventilator selection using the developed CIFDPWA and CIFDPWG based on the MCDM approach. We found that GE Healthcare is the best alternative using the CIFDPWA, while Medtronic is the best option using the CIFDPWG operator. To check the applicability of the developed AOs, we made a detailed comparison with some other existing AOs. Finally, it offers some firm conclusions.