A Unified Framework of Fuzzy Neutrosophic Supra Set , Turiyam  Set For Advanced Medical Diagnosis

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 supra set, fuzzy decision making, Medical diagnosis under uncertainty, Indeterminacy modeling and knowledge representation, fuzzy neutrosophic turiyam set.

Abstract

In this paper focus of the fuzzy neutrosophic supra set is an advanced mathematical
concept that merges fuzzy set theory, neutrosophic logic and supra topology to address uncertainty,
vagueness and indeterminacy more effectively than classical structures. Decision algorithms based
on neutrosophic supra sets can distinguish between symptoms and test results with varying
certainty, improving diagnostic accuracy under uncertainty. A topological structure on fuzzy
neutrosophic supra set is considered as a tool to derive some characterizations of these concept.
Also we define a Fuzzy Neutrosophic Turiyam Set as an extension and apply to decision making
problem. However, in highly complex real-world problems such as medical diagnosis, multi-criteria
decision making, and Social Sciences- the classical neutrosophic approach still faces limitations
when information extends beyond truth, indeterminacy, and falsity. To overcome this, the concept
of the Turiyam set has been proposed. Analogously, a Fuzzy Neutrosophic Turiyam Set (FNTS)
introduces a fourth dimension to the neutrosophic structure. Along with truth (T), indeterminacy (I),
and falsity (F), the Turiyam component (Y) represents situations that transcend the known triad -
capturing unknown, transcendental, or beyond-human-perception states of information. This
framework is particularly powerful in medical diagnosis, where certain symptoms and disease
relations cannot be explained merely by true/false or uncertain values, but require a fourth
dimension to represent “unexplored” or “beyond - known” medical states.