Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2602.14128

Fuzzy Aura Topological Spaces with Applications to Rough Set Theory and Medical Decision Making

Açıkgöz
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

math.GN

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Açıkgöz. 2026-02-15. Fuzzy Aura Topological Spaces with Applications to Rough Set Theory and Medical Decision Making. https://arxiv.org/abs/2602.14128

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Sobriety of Scott topologies under countability conditions

In this paper, we focus on the sobriety of the Scott topology in countable case. Specifically, we show that: (1) every meet-continuous core-compact countable dcpo is sober with respect to the Scott topology; (2)every countable locally compact dcpo is sober endowed with the Scott topology; (3) the lattice of all open sets for the rational numbers space Q equipped with the Scott topology is not sober.

math.GN↗
arXiv2026

Exponentiable Objects and Function spaces in Lowen Fuzzy Topological Spaces

We study exponentiable objects and function spaces in the category of stratified Lowen fuzzy topological spaces over \(\I=[0,1]\). Using the Lowen fuzzy Sierpiński object \(\Sier\), which identifies \(τ_X\) with \(C(X,\Sier)\), we explicitly determine the largest splitting topology on this mapping set. Its open weights \(Φ:τ_X\to\I\) are precisely those satisfying Scott continuity and a finite-tier compatibility condition induced by finite powers of \(\Sier\). This yields an intrinsic characterization: \(X\) is exponentiable if and only if every \(μ\inτ_X\) satisfies \[ μ=\bigvee_{λ\triangleleftΦ} (\const{Φ(μ)}\wedgeλ), \qquad λ\triangleleftΦ \Longleftrightarrow \const{Φ(ν)}\wedgeλ\leqν \quad(ν\inτ_X). \] When this condition holds, \(Y^X\) has underlying set \(C(X,Y)\), with topology generated by \([Φ,v](f)=Φ(v\circ f)\). We also obtain a dual closed-set formulation and three applications. Exponentiability implies that \(τ_X\) is a continuous lattice, although the converse fails. Moreover, a classical space \(X\) is exponentiable exactly when its induced fuzzy space \(ωX\) is exponentiable in the entire stratified Lowen category. Finally, Lowen compact, strongly fuzzy compact, and \(N\)-compact Hausdorff spaces are exponentiable.

math.GN↗
arXiv2026

Super calibers in topological spaces and topological hyperspaces

We study the notion of a super caliber of a topological space, which is closely related to the classical notion of caliber and has appeared in the literature under several different names. We collect and unify several known results and establish new results concerning the collections of super calibers of topological spaces and their hyperspaces. In particular, we investigate the relationship between the super calibers of a space $X$ and those of hyperspaces $\mathcal{H}(X)$ lying between $\mathrm{CL}(X)$ and $\mathcal{F}(X)$. For infinite metrizable spaces, we characterize several cases in which $\mathsf{SC}(X)$ and $\mathsf{SC}(\mathrm{CL}(X))$ differ and establish an independence result over \textsf{ZFC}; see Theorem~5.12.

math.GN↗