On the hyperspace of bounded closed sets under a generalized Hausdorff stationary fuzzy metric

Dong Qiu; Chongxia Lu; Shuai Deng; Liang Wang

Kybernetika (2014)

  • Volume: 50, Issue: 5, page 758-773
  • ISSN: 0023-5954

Abstract

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In this paper, we generalize the classical Hausdorff metric with t-norms and obtain its basic properties. Furthermore, for a given stationary fuzzy metric space with a t-norm without zero divisors, we propose a method for constructing a generalized Hausdorff fuzzy metric on the set of the nonempty bounded closed subsets. Finally we discuss several important properties as completeness, completion and precompactness.

How to cite

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Qiu, Dong, et al. "On the hyperspace of bounded closed sets under a generalized Hausdorff stationary fuzzy metric." Kybernetika 50.5 (2014): 758-773. <http://eudml.org/doc/262158>.

@article{Qiu2014,
abstract = {In this paper, we generalize the classical Hausdorff metric with t-norms and obtain its basic properties. Furthermore, for a given stationary fuzzy metric space with a t-norm without zero divisors, we propose a method for constructing a generalized Hausdorff fuzzy metric on the set of the nonempty bounded closed subsets. Finally we discuss several important properties as completeness, completion and precompactness.},
author = {Qiu, Dong, Lu, Chongxia, Deng, Shuai, Wang, Liang},
journal = {Kybernetika},
keywords = {Hausdorff metric; hyperspace; triangular norms; stationary fuzzy metric; Hausdorff metric; hyperspace; triangular norms; stationary fuzzy metric},
language = {eng},
number = {5},
pages = {758-773},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the hyperspace of bounded closed sets under a generalized Hausdorff stationary fuzzy metric},
url = {http://eudml.org/doc/262158},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Qiu, Dong
AU - Lu, Chongxia
AU - Deng, Shuai
AU - Wang, Liang
TI - On the hyperspace of bounded closed sets under a generalized Hausdorff stationary fuzzy metric
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 5
SP - 758
EP - 773
AB - In this paper, we generalize the classical Hausdorff metric with t-norms and obtain its basic properties. Furthermore, for a given stationary fuzzy metric space with a t-norm without zero divisors, we propose a method for constructing a generalized Hausdorff fuzzy metric on the set of the nonempty bounded closed subsets. Finally we discuss several important properties as completeness, completion and precompactness.
LA - eng
KW - Hausdorff metric; hyperspace; triangular norms; stationary fuzzy metric; Hausdorff metric; hyperspace; triangular norms; stationary fuzzy metric
UR - http://eudml.org/doc/262158
ER -

References

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