On Fuzzy Neutrosophic Turiyam Sets In Fourth- Dimensional Data Space And Its Applications

Abstract

Modeling uncertainty in high-dimensional systems requires frameworks that extend beyond binary and ternary logic. This paper discusses the Fuzzy Neutrosophic Turiyam Set (FNTS), a four-dimensional extension of classical neutrosophic sets, incorporating a new Turiyam (Y) component to capture latent restorative potential and meta-cognitive uncertainty. We formally define FNTS algebraic operations, including union, intersection, and complement, and propose the Turiyam Einstein Weighted Averaging Operator (TEWA) for non-linear aggregation. Empirical validation using multi-phase sleep state modeling demonstrates that FNTS achieves a 25% percentage gain in descriptive dimensionality compared to classical neutrosophic sets, enabling finer differentiation of hidden states, including deep sleep restoration and REM cognitive integration. The results confirm FNTS as a mathematically rigorous and practically effective paradigm for uncertainty modeling in complex multi-source environments.