Exploring <i>n</i> ‐Dimensional Fuzzy Soft Sets: A Framework for Multicriteria Decision‐Making Problems

This study introduces several operations on n ‐dimensional fuzzy sets, including union, intersection, and complement, and examines the validity of De Morgan’s law within this framework. To further elucidate the conceptual underpinnings, the study also presents illustrative examples of t ‐norm, t ‐conorm, and negation operations on n ‐dimensional fuzzy sets. Furthermore, the paper proposes a novel structure termed the n ‐dimensional fuzzy soft sets, which extends the concepts of both soft sets and n ‐dimensional fuzzy sets. The foundational properties of n ‐dimensional fuzzy soft sets are explored in detail, and various operations such as union, intersection, negation, t ‐norms, and t ‐conorms are defined and analyzed within this context. Additionally, the study discusses relevant laws, including De Morgan’s law as they pertain to the proposed structure. To demonstrate the practical utility of this new model, the study presents its application in decision‐making scenarios, such as the selection of the most suitable vendor for a critical project. A comparative analysis with existing decision‐making strategies based on intuitionistic fuzzy soft sets and interval‐valued fuzzy soft sets highlights the enhanced effectiveness and robustness of the proposed methodology.