Abstract:
A Generalizations of Zadeh's Fuzzy Set Theory have consistently sought more powerful tools to model imprecision. Following the path from Fuzzy Metric Spaces to Park's Intuitionistic Fuzzy Metric Spaces, we introduce a significant leap forward: the q- Rung Orthopair Fuzzy (q-ROF) Metric Space. This novel qROF framework provides a superior analytical structure that directly addresses the limitations of existing models. Unlike previous versions, the q-ROF model greatly expands the permissible range for non-membership and membership grades. We illustrate this with a detailed example, showing how the q-ROF metric substantially increases the allowable selection and membership space, which is often restricted in the intuitionistic context. The paper fully defines the q-ROF metric space with clear examples and establishes its core topological characteristics, including the properties of open balls and convergence. Furthermore, we introduce the concept of q-ROF Menger boundedness. Crucially, the mathematical robustness of our generalization is confirmed by establishing fundamental theorems, including Baire's Theorem and the Uniform Limit Theorem, within the q-ROF metric space perspective. This work provides a powerful, generalized foundation for future research in topology, fixed point theory, and computational decision science.
Page(s):
141-141
DOI:
DOI not available
Published:
Journal: 4th International Conference of Sciences “Revamped Scientific Outlook of 21st Century, 2025” , November 12,2025, Volume: 1, Issue: 1, Year: 2025