2026/02/15 by Açıkgöz · 1 voice · 2 citations
Mathematics · #math.GN
We introduce the concept of a fuzzy aura topological space (X, τ, a), obtained by equipping a Chang-type fuzzy topological space (X, τ) with a fuzzy scope function a : X → τ satisfying a(x)(x) = 1 for every x ∈ 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.