TURK 2025

This paper is devoted to the investigation of soft Lie hypergroup, which combines the foundational aspects of Lie hypergroups with the parameterization and uncertainty-handling capabilities of soft set theory. The soft set theory, originally introduced to handle imprecise or uncertain information, is utilized here to introduce variability and parameterization into the operation of hypergroups. This approach allows for the creation of an algebraic system capable of accommodating the inherent vagueness and complexity often found in real-world applications, where precise data or clear-cut boundaries are not always available. The resulting soft Lie hypergroup provides a richer and more adaptable structure compared to classical Lie hypergroups. Several representative examples are constructed to illustrate the behavior and utility of soft Lie hypergroups in both abstract and concrete cases. Also, the category of soft Lie hypergroups is constructed. The formulation of this category facilitates a systematic approach to understanding the morphisms between different soft Lie hypergroups and establishes a foundational framework for further categorical investigations into the properties of soft algebraic structures. Finally, the study explores essential substructures, such as soft sub-hypergroups providing a detailed analysis of their properties. Through its novel approach, this paper contributes to the advancement of soft algebraic theory, providing a comprehensive foundation for future investigations and applications. The work encourages further study into the interplay between soft set theory, Lie theory and hypergroup theory.