A Theoretical Framework for Functions Mapping Complex Numbers to Fuzzy Sets

In order to bridge the gap between classical complex analysis and fuzzy mathematics, this work presents a new theoretical basis for functions that convert complex numbers into fuzzy sets. Fuzzyfied complex valued mappings, continuity, convergence, and analytic property adoption in fuzzy environments are the main points of the system. The link between complex moduli and fuzzy membership gradations is investigated in this paper by combining topological and algebraic ideas. Potentially useful in signal processing, decision theory, and AI, the suggested model allows for a more thorough understanding of uncertainty quantification in complex-valued systems. Strengthening the connection between complex function theory and soft computing paradigms, this analysis establishes a foundation for future studies on integration, differentiability, and fuzzy holomorphy.