A Novel Neutrosophic Multi-Layered Complex Refined Hyperstructure: Theoretical Advancement with Illustrative Examples from Employee Mental Health Education Effectiveness in Enterprises - Min Zhang; Yaozu Wang; Rui Huang; Qiao Wu; Bingqing Li (Neutrosophic Sets and Systems)
This paper introduces a new theoretical structure in neutrosophic set theory called the Neutrosophic Multi-Layered Complex Refined Hyperstructure (NMCRH). It is a formal extension of Single-Valued Complex Refined Neutrosophic Sets (SVCRNS) and Subset-Valued Complex Refined Neutrosophic Sets (SSVCRNS), defined by multiple interconnected layers of refined truth, indeterminacy, and falsity, each expressed as complex subset-valued functions. Unlike earlier models, NMCRH incorporates inter-layer projection functions that enable logical transitions between neutrosophic layers, forming a multi-level hyperstructure. Each projection uses weighted complex coefficients, making the structure highly adaptable and expressive in modeling uncertainty and logical multiplicity. The paper focuses strictly on theoretical development, providing full mathematical definitions, structured equations, and formal proofs. However, to aid understanding and interpretation, detailed numerical examples are presented using realworld-inspired scenarios from employee mental health education in enterprises (LIU). These examples demonstrate how neutrosophic complexity can be used to reflect layered psychological states, varied perceptual truths, and conflicting mental attitudes under educational programs. This framework offers a significant advancement in neutrosophic theory, providing a logically consistent, non-temporal, and highly extensible foundation for future work in logic, cognition, and uncertainty modeling.