Weighted correlation coefficients for q-rung orthopair fuzzy sets with application in multi-criteria decision-making

<h2>Abstract</h2> Correlation coefficients (CCs) have been widely used to assess the relationships between fuzzy sets (FSs) in the literature. A q-rung orthopair fuzzy set (q-ROFS) is an advanced extension of FSs that offers a robust and comprehensive framework for representing uncertain and vague information. In this paper, we introduce a new weighted CCs for q-ROF environment, enhancing their ability to model complex uncertainty. Additionally, we define the degree of favor for q-ROFSs, providing a novel approach for handling fuzzy data. Multi-criteria decision-making (MCDM) serves as a powerful tool for decision makers to identify the best possible choice among available alternatives based on gathered information. In many real-world MCDM scenarios, the criteria weights are often unknown, which poses a challenge for methods that rely on user-defined weights. This highlights the need to develop a reliable approach for determining these weights. To address this, we propose a weight calculation schema based on the degree of favor of a criterion within a q-ROFS, offering a systematic way to estimate these unknown weights. Furthermore, we present a ranking method that leverages the proposed weighted CCs and weight calculation schema to effectively rank alternatives. This enables decision makers to not only select the best option but also prioritize the remaining choices. In doing so, we give a novel q-ROFS-based fuzzy MCDM approach, providing a fresh perspective on decision-making under fuzzy environment. Finally, we validate the practical applicability and innovation of our method by applying it to two real MCDM scenarios. We also demonstrate its versatility by showcasing real examples for two special cases, intuitionistic FSs and Pythagorean FSs, and compare the results with existing methods to highlight its superiority.