q -Rung Orthopair Picture Fuzzy Topological Spaces and Parameter-Dependent Continuity: Control System Applications

Abstract

This paper presents novel concepts in fuzzy topologies, namely q -rung orthopair picture fuzzy ( q -ROPF) topology and q -rung orthopair picture fuzzy point ( q -ROPFP). These concepts extended the existing notions in fuzzy topologies. We introduced a more relaxed form of continuity, called q ε -ROPF continuity, which allows for a flexible analysis of functions between q -ROPF topological spaces by incorporating an error bound ε . We define the q -neighborhood system for a q -ROPF point in a q -ROPF topological space and investigate the convergence of sequences of such points. Our results shed light on the behavior of functions and sequences in these spaces, as well as the conditions for uniqueness of limits within the realm of supports. This research has practical implications in control systems, providing valuable insights into the stability and robustness of the control strategies in the presence of small changes represented by the epsilon value.