Exploring complex n,m-rung orthopair fuzzy aggregation operators for enhanced multi-attribute decision making

The recently introduced n,m-rung orthopair fuzzy set emerges as a valuable means to articulate ambiguity and vagueness. With its enhanced capacity to handle uncertain scenarios in contrast to q-rung orthopair fuzzy set theories, n,m-rung orthopair fuzzy sets find diverse applications in everyday decision-making processes. This study presents a fresh approach to handling ambiguity and uncertainty in multi-attribute decision-making by introducing a novel tool termed as complex n,m-rung orthopair fuzzy set (Cn,m-ROFS). The proposed Cn,m-ROFS integrates the advantages of n,m-rung orthopair fuzzy set and captures both quantitative and qualitative analyses of decision-makers. This model represents a significant advancement over complex q-rung orthopair fuzzy sets and offers a fruitful avenue for addressing such complexities in decision-making processes. Moreover, the fundamental laws of Cn,m-ROFSs are outlined. Additionally, the paper develops specialized score functions, accuracy functions, and comparison methods tailored for two complex n,m-rung orthopair fuzzy numbers. Furthermore, it explores novel aggregation operators such as complex n,m-rung orthopair fuzzy weighted averaging (Cn,m-ROFWA) and complex n,m-rung orthopair fuzzy weighted geometric (Cn,m-ROFWG) operators based on Cn,m-ROFSs, providing comprehensive descriptions of their properties. Utilizing these operators, a new method for multi-attribute decision making problems within the complex n,m-rung orthopair fuzzy set theory framework is presented and validated through practical examples. The paper’s findings underscore the effectiveness and practical applicability of the proposed method compared to existing methodologies, shedding light on its practical utility and efficacy.