Rula Ismael Hamad

Abstract:

This present research paper introduces Fuzzy Complex Valued Metric Spaces, which are novel extensions of classical metric spaces embedding both fuzziness and complex-valued distances in a unique way. FCVMS embeds all the uncertainty handling capabilities of fuzzy metric spaces along with multi-dimensional phase and magnitude relationships that are inherent in complex-valued metrics. Properties which form the topological structure of FCVMS include open and closed sets, interior, closure, boundary, behavior of sequences w.r.t. convergence, completeness, compactness, separability, and connectedness. As for a number of case studies to show the applicability of FCVMS, two have been carried out: the first relates to modeling uncertainty and oscillations in control systems, while the second concerns simulating sensor networks, where both imprecise measurement and periodic signal fluctuations form an essential issue.

Graphs and numerical simulations provide an idea of how FCVMS can model a system better than other conventional metrics. The results show that FCVMS is a strong framework for analyzing systems that are dynamic, uncertain, and phase-sensitive; they range from engineering and telecommunications to environmental monitoring.