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  4. Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics
  5. Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.30 (1999) s.
  6. Fuzziness in Chang's fuzzy topological spaces
 
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Fuzziness in Chang's fuzzy topological spaces

Gregori, Valentín
•
Vidal, Anna
1999
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ISSN
0049-4704
http://hdl.handle.net/10077/4343
  • Article

Abstract
It is known that fuzziness within the concept of openness of a fuzzy set in a Chang's fuzzy topological space (fts) is absent. In this paper we introduce a gradation of openness for the open sets of a Chang jts (X, $\mathcal{T}$) by means of a map $\sigma\;:\; I^{x}\longrightarrow I\left(I=\left[0,1\right]\right)$, which is at the same time a fuzzy topology on X in Shostak 's sense. Then, we will be able to avoid the fuzzy point concept, and to introduce an adeguate theory for $\alpha$-neighbourhoods and $\alpha-T_{i}$ separation axioms which extend the usual ones in General Topology. In particular, our $\alpha$-Hausdorff fuzzy space agrees with $\alpha${*} -Rodabaugh Hausdorff fuzzy space when (X, $\mathcal{T}$) is interpreservative or $\alpha$-locally minimal.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
30 (1999) suppl.
Subjects
  • fuzzy topology

  • gradation of openness...

  • fuzzy point

Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
Valentín Gregori and Anna Vidal, "Fuzziness in Chang's fuzzy topological spaces", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 30 (1999) suppl., pp. 111-121.
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