A continuous operator extending fuzzy ultrametrics

I. Stasyuk; Edward D. Tymchatyn

Commentationes Mathematicae Universitatis Carolinae (2011)

  • Volume: 52, Issue: 4, page 611-622
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Stasyuk, I., and Tymchatyn, Edward D.. "A continuous operator extending fuzzy ultrametrics." Commentationes Mathematicae Universitatis Carolinae 52.4 (2011): 611-622. <http://eudml.org/doc/246123>.

@article{Stasyuk2011,
abstract = {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.},
author = {Stasyuk, I., Tymchatyn, Edward D.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {fuzzy ultrametric; continuous extension operator; Hausdorff metric; fuzzy ultrametric; continuous extension operator; Hausdorff metric},
language = {eng},
number = {4},
pages = {611-622},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A continuous operator extending fuzzy ultrametrics},
url = {http://eudml.org/doc/246123},
volume = {52},
year = {2011},
}

TY - JOUR
AU - Stasyuk, I.
AU - Tymchatyn, Edward D.
TI - A continuous operator extending fuzzy ultrametrics
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 4
SP - 611
EP - 622
AB - 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.
LA - eng
KW - fuzzy ultrametric; continuous extension operator; Hausdorff metric; fuzzy ultrametric; continuous extension operator; Hausdorff metric
UR - http://eudml.org/doc/246123
ER -

References

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