A Novel Approach to the Vectorial Redefinition of Ordered Fuzzy Numbers for Improved Arithmetic and Directional Representation

This paper presents a novel formulation of Ordered Fuzzy Numbers (OFNs), referred to as Vectorial Ordered Fuzzy Numbers (vOFNs). In contrast to the traditional definition based on a pair of functions, the vOFN framework employs a pair of vectors, offering a more concise and structurally coherent representation. This reformulation addresses the key limitations of classical OFNs, such as non-convexity and difficulties in handling curvilinear boundaries during multiplication and division. The vOFN model retains compatibility with commonly used fuzzy number types-triangular, trapezoidal, and singleton-and preserves directional properties that are essential for modeling fuzzy trends. Furthermore, it simplifies comparison operations and supports a complete algebraic structure. Due to its mathematical consistency, low computational complexity, and ease of implementation, the vOFN framework is well-suited for applications in intelligent systems, particularly in domains that require reasoning under uncertainty.