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On The Fuzzy Topological Spaces Based On A Fuzzy Space (X,I) |
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PP: 1295-1301 |
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doi:10.18576/amis/180611
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Author(s) |
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Ibrahim Jawarneh,
Abd Ulazeez Alkouri,
Jehad AlJaraden,
Bilal N. Al-Hasanat,
Mohammad Hazaimeh,
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Abstract |
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| The fuzzy set (\( \mathcal{FS} \)) $X$ is a class of objects associated by a membership that assigns each element of $X$ a grade value ( or values) in the closed interval $I = [0,1]$. Such a set defines a new type of topology called fuzzy topology (\( \mathcal{FT} \)). There are many definitions for the \(\mathcal{FT}\), one of these definitions is Dips definition that introduced the fuzzy space (\(\mathcal{FS_{P}}\)) $(X,I)$ as a set of fuzzy subspaces (\(\mathcal{F_{S}S}\)), and defined \(\mathcal{FT}\) on the fuzzy space (\(\mathcal{FS_{P}}\)) $(X,I)$ which we study and develop in this paper. Various kinds of fuzzy topological spaces (\( \mathcal{FTS} \)) on the \( \mathcal{FS_{P}} \) $(X,I)$ are defined and explained in this article, for example, cofinite ( and cocountable ) \( \mathcal{FT} \), left ( and right ) ray \(\mathcal{FT}\), and standard \(\mathcal{FT}\). The fuzzy point (\(\mathcal{FP}\)) is studied and classified. So the exterior, interior, boundary, dense, and isolated \(\mathcal{FP}\) are defined, and we apply some theorems on them. Furthermore, fuzzy separation axioms are presented with illustrated examples.
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