Fuzzy Aura Topological Spaces with Applications to Rough Set Theory and Medical Decision Making
Açıkgöz
TL;DR
This work develops a comprehensive framework of fuzzy aura topological spaces by coupling a Chang-type fuzzy topology with a fuzzy scope function, yielding fuzzy aura-closure and -interior operators, a fuzzy aura topology, and a transfinite closure to a fuzzy Kuratowski operator. It then builds a complete hierarchy of five generalized fuzzy open-set classes, analyzes fuzzy aura-continuity and separation, and defines fuzzy aura-based rough approximations that unify crisp aura and the Dubois–Prade models. The theory is paired with a data-driven FA-MCDM algorithm for medical diagnosis, validated on the De et al. benchmark with robust sensitivity analyses across varying weights and the caution parameter $\alpha$, and provides uncertainty quantification through aura-based boundaries. The results offer a topology-backed, uncertainty-aware approach to rough-set-inspired decision making with practical impact in medical diagnostics and potential extensions to soft and neutrosophic aura frameworks.
Abstract
We introduce the concept of a fuzzy aura topological space $(X, \tildeτ, \tilde{a})$, obtained by equipping a Chang-type fuzzy topological space $(X, \tildeτ)$ with a fuzzy scope function $\tilde{a} : X \to \tildeτ$ satisfying $\tilde{a}(x)(x) = 1$ for every $x \in X$. This framework generalizes the recently introduced (crisp) aura topological spaces to the fuzzy setting. We define the fuzzy aura-closure operator and the fuzzy aura-interior operator, and prove that the closure is a fuzzy additive Čech closure operator whose transfinite iteration yields a fuzzy Kuratowski closure. Five classes of generalized fuzzy open sets are introduced, and a complete hierarchy among them is established with counterexamples separating all distinct classes. Fuzzy aura-continuity and its decompositions are studied. Separation axioms and fuzzy aura-regularity are introduced. Fuzzy aura-based lower and upper approximation operators are defined, generalizing both the crisp aura rough set model and the Dubois-Prade fuzzy rough set model. A novel FA-MCDM algorithm is proposed and applied to a medical diagnosis problem with comprehensive sensitivity analysis.