Advanced Intuitionistic Fuzzy Weighted Geometric Aggregation Operator for the Intuitionistic Fuzzy Numbers and Its Application to Multi-attribute Decision-making

In complex and uncertain scenarios, multi-attribute decision-making (MADM) presents a significant challenge, especially when existing MADM approaches fail to distinguish among the ranking orders (ROs) of alternatives. An important tool to address such challenges is the use of aggregation operators (AOs), which integrate multiple input values into a single representative output. Therefore, in this study, we introduce new operational laws for intuitionistic fuzzy numbers (IFNs) and propose an advanced intuitionistic fuzzy weighted geometric (AIFWG) AO for aggregating IFNs. We also investigate essential properties of the proposed AIFWG AO, such as idempotency, monotonicity, and boundedness. These properties confirm the reliability of the proposed AIFWG AO, making it well-suited for real-life decision-making applications. Building on this, we present a new MADM approach under the IFN framework using the proposed AIFWG AO. To validate the effectiveness and robustness of the proposed MADM approach, we solve three MADM problems. The outcomes clearly demonstrate that our method not only addresses the shortcomings of existing MADM approaches but also provides a more reliable ranking of alternatives in uncertain situations.