A Novel p-Norm-Based Ranking Algorithm for Multiple-Attribute Decision Making Using Interval-Valued Intuitionistic Fuzzy Sets and Its Applications

The main focus of this paper is to introduce an algorithm that enhances the outcomes of multiple-attribute decision making by harnessing the adaptability of interval-valued intuitionistic fuzzy (IVIF) sets (IVIFSs). This algorithm utilizes IVIF numbers (IVIFNs) to represent attribute values and attribute weights, enabling the decision maker to account for the intricate nuances and uncertainties that are inherent in the decision-making process. We introduce a novel generalized score function (GSF) designed to overcome the limitations of previous functions. This function incorporates two parameters, denoted as γ1andγ2(γ1+γ2=1) with γ1∈(0,0.5). The core concept of this algorithm centers around the computation of the p-distance for each alternative relative to the positive ideal alternative. The p-distance is derived from the p-norm associated with each alternative’s score matrix, providing the decision maker (DM) with a tool to rank the available alternatives. Various examples are given to demonstrate the practicality and effectiveness of the proposed algorithm. Additionally, we apply the algorithm to a real event-based multiple-attribute decision-making (MADM) problem—the investment company problem—to identify the optimal alternatives through a comparative analysis.