A Novel Neutrosophic Multi-Layered Complex Refined Hyperstructure: Theoretical Advancement with Illustrative Examples from Employee Mental Health Education Effectiveness in Enterprises

Abstract

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 real
world-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. 

DOI: 10.5281/zenodo.15625235