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

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 triadcapturing 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.