Fuzzy Aura Topological Spaces with Applications to Rough Set Theory and Medical Decision Making
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908835359227904 |
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| author | Açıkgöz |
| author_facet | Açıkgöz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14128 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fuzzy Aura Topological Spaces with Applications to Rough Set Theory and Medical Decision Making Açıkgöz General Topology 54A40, 54A05, 03E72, 54C08, 54D10, 90B50 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. |
| title | Fuzzy Aura Topological Spaces with Applications to Rough Set Theory and Medical Decision Making |
| topic | General Topology 54A40, 54A05, 03E72, 54C08, 54D10, 90B50 |
| url | https://arxiv.org/abs/2602.14128 |