Fuzzy Neutrosophic Turiyam Sets Diagrammatic and  Operational Analysis with Real World Applications

Poongothai Eswaran; Balaganesan Palanivelu; Florentin Smarandache

Authors

Poongothai Eswaran Department of Mathematics, AMET University, Chennai, Tamilnadu, India;
Balaganesan Palanivelu Department of Mathematics, AMET University, Chennai, Tamilnadu, India;
Florentin Smarandache Emeritus Professor, Physical and Natural Sciences Division University of New Mexico, Gallup, NM, USA

Keywords:

Fuzzy Neutrosophic Turiyam Set (FNTS), open set, closed set, interior, closure, uncertainty modelling, medical diagnosis, intelligent decision support.

Abstract

In this paper, the fourth dimension of neutrosophy, that of "Turiyam," is examined as it
symbolizes the "absolute" or "transcendental" essence that preexists and permeates the truth triad,
indeterminacy, and the falsity trio. Although the current state of Neutrosophic Sets works perfectly
to represent the notion of "ambiguity," they are inefficient in incorporating the essence wherein
such truth measures oscillate. Thus, the proposed model, Fuzzy Neutrosophic Turiyam Set (FNTS),
will have its corresponding algebraic operator functions and "Law of Turiyam Non-Exclusion."
Moreover, models involving distance function in four-dimensional space as well as the
hyper-polyhedron will be considered. Quantum computing applications and modeling of
socioeconomic "Black Swan" events validate that the proposed FNTS model is significantly more
stable in chaotic situations than the current models proposed for neutrosophic settings.

DOI 10.5281/zenodo.18882822