فهرست نشریات علمی دسترسی آزاد ایران

The main results of this paper involve the development of a novel theoretical framework by integrating interval-valued m-polar fuzzy (IV mP F) sets into the structure of ordered semigroups. This integration enhances the ability to model complex systems characterized by uncertainty, imprecision, ordered data, and multi-polarity, which are critical in real-world decision-making scenarios. Specifically, the study defines and explores IV mP F sets, IV mP F ideals, IV mP F bi-ideals, and IV mP F quasi-ideals, providing concrete examples to illustrate their algebraic structure within ordered semigroups. The relationships between these IV mP F constructs are thoroughly examined, and their definitions are expressed in terms of classical ideals, quasi-ideals, and bi-ideals. These findings not only advance the theoretical understanding of algebraic structures under uncertainty but also provide practical tools for applications in multi-criteria decision-making, optimization, and artificial intelligence, offering new avenues for solving complex real-world problems. The scope involves integrating IV mP F sets into ordered semigroups to model complex systems with uncertainty and multi-polarity, while limitations include the need for real-world validation and challenges in scaling to highly complex or dynamic systems.