Probabilistic uniformization of fuzzy topologies

doi:10.1016/0165-0114(78)90021-0

Fuzzy Sets and Systems

Volume 1, Issue 4, October 1978, Pages 311-332

https://doi.org/10.1016/0165-0114(78)90021-0 Get rights and content

Abstract

Extending the concept of probabilistic metrics to probabilistic uniformities we establish a necessary and sufficient condition, under which fuzzy topologies are probabilistically uniformisable. Applications of this result to normal fuzzy topologies are also given.

References (24)

C.L. Chang
Fuzzy topological spaces
J. Math. Anal. Appl.
(1968)
J.A. Goguen
L-fuzzy sets
J. Math. Anal. Appl.
(1967)
J.A. Goguen
The fuzzy Tychonoff theorem
J. Math. Anal. Appl.
(1973)
B. Hutton
Normality in fuzzy topological spaces
J. Math. Anal. Appl.
(1975)
B. Hutton
Uniformities on fuzzy topological spaces
J. Math. Anal. Appl.
(1977)
R. Lowen
Fuzzy topological spaces and fuzzy compactness
J. Math. Anal. Appl.
(1976)
R. Lowen
Fuzzy topological spaces and fuzzy compactness
J. Math. Anal. Appl.
(1976)
G. Birkhoff
Lattice Theory
N. Bourbaki
Eléments de mathématiques
L. Fuchs
Teilweise geordnete algebraische Strukturen
(1966)
U. Höhle, Probabilistische Metriken auf der Menge der nicht negativen Verteilungsfunktionen, Aequationes Math. (to...

U. Höhle, Probabilistische Topologien, Manuscripta Math....

I. Kramosil et al.

Fuzzy metrics and statistical metric spaces

Kybernetika

(1975)

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Probabilistic uniformization of fuzzy topologies

Abstract

J. Math. Anal. Appl.

J. Math. Anal. Appl.

J. Math. Anal. Appl.

J. Math. Anal. Appl.

J. Math. Anal. Appl.

J. Math. Anal. Appl.

J. Math. Anal. Appl.

Lattice Theory

Eléments de mathématiques

Teilweise geordnete algebraische Strukturen

Fuzzy metrics and statistical metric spaces

Kybernetika