Geodesic
A continuous operator extending fuzzy ultrametrics
Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 4, pp. 611-622 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We consider the problem of simultaneous extension of fuzzy ultrametrics defined on closed subsets of a complete fuzzy ultrametric space. We construct an extension operator that preserves the operation of pointwise minimum of fuzzy ultrametrics with common domain and an operation which is an analogue of multiplication by a constant defined for fuzzy ultrametrics. We prove that the restriction of the extension operator onto the set of continuous, partial fuzzy ultrametrics is continuous with respect to the Hausdorff metric topology.
We consider the problem of simultaneous extension of fuzzy ultrametrics defined on closed subsets of a complete fuzzy ultrametric space. We construct an extension operator that preserves the operation of pointwise minimum of fuzzy ultrametrics with common domain and an operation which is an analogue of multiplication by a constant defined for fuzzy ultrametrics. We prove that the restriction of the extension operator onto the set of continuous, partial fuzzy ultrametrics is continuous with respect to the Hausdorff metric topology.
Classification : 54A40, 54C20, 54E70
Keywords: fuzzy ultrametric; continuous extension operator; Hausdorff metric 
@article{CMUC_2011_52_4_a10,
     author = {Stasyuk, I. and Tymchatyn, E. D.},
     title = {A continuous operator extending fuzzy ultrametrics},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {611--622},
     year = {2011},
     volume = {52},
     number = {4},
     mrnumber = {2864002},
     zbl = {1249.54018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2011_52_4_a10/}
}
TY  - JOUR
AU  - Stasyuk, I.
AU  - Tymchatyn, E. D.
TI  - A continuous operator extending fuzzy ultrametrics
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2011
SP  - 611
EP  - 622
VL  - 52
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMUC_2011_52_4_a10/
LA  - en
ID  - CMUC_2011_52_4_a10
ER  - 
%0 Journal Article
%A Stasyuk, I.
%A Tymchatyn, E. D.
%T A continuous operator extending fuzzy ultrametrics
%J Commentationes Mathematicae Universitatis Carolinae
%D 2011
%P 611-622
%V 52
%N 4
%U http://geodesic.mathdoc.fr/item/CMUC_2011_52_4_a10/
%G en
%F CMUC_2011_52_4_a10
Stasyuk, I.; Tymchatyn, E. D. A continuous operator extending fuzzy ultrametrics. Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 4, pp. 611-622. http://geodesic.mathdoc.fr/item/CMUC_2011_52_4_a10/