A Generalized Complex Fuzzy Representation Space: Metric Structures, Fixed-Point Analysis, and Applications to Uncertain Complex Systems

Ravi Shanker Kumar

Abstract: The integration of complex analysis with fuzzy set theory provides an e?ective mathematical framework for representing uncertain complex-valued information arising in engineering, computational intelligence, and decision sciences. This article introduces a new Generalized Complex Fuzzy Representation Operator (GCFRO) that transforms each complex number into a fuzzy structure characterized by a nonlinear distance-based membership mechanism. A Generalized Complex Fuzzy Representation Space (GCFRS) is constructed, and a novel fuzzy metric is proposed to quantify the similarity between complex fuzzy objects. Theoretical investigations establish fundamental properties including boundedness, invariance, continuity, stability, completeness, compactness, and convergence. Furthermore, a generalized contraction operator and a Banach-type fixed-point theorem are developed to guarantee the existence and uniqueness of stable fuzzy transformations. Numerical examples and applications to uncertain signal processing, noise-resilient information representation, and complex-valued intelligent systems demonstrate the e?ectiveness of the proposed framework. The obtained results provide a new mathematical direction for the integration of complex numbers and fuzzy uncertainty models.

Keywords: Complex fuzzy representation, Fuzzy metric space, Fixed-point theory, Complex uncertainty, Intelligent fuzzy systems

How to Cite?: Ravi Shanker Kumar, "A Generalized Complex Fuzzy Representation Space: Metric Structures, Fixed-Point Analysis, and Applications to Uncertain Complex Systems", Volume 15 Issue 6, June 2026, International Journal of Science and Research (IJSR), Pages: 1272-1288, https://www.ijsr.net/getabstract.php?paperid=SR26624164731, DOI: https://dx.doi.org/10.21275/SR26624164731

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