The strongest t-norm for fuzzy metric spaces

Dong Qiu; Weiquan Zhang

Kybernetika (2013)

  • Volume: 49, Issue: 1, page 141-148
  • ISSN: 0023-5954

Abstract

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In this paper, we prove that for a given positive continuous t-norm there is a fuzzy metric space in the sense of George and Veeramani, for which the given t-norm is the strongest one. For the opposite problem, we obtain that there is a fuzzy metric space for which there is no strongest t-norm. As an application of the main results, it is shown that there are infinite non-isometric fuzzy metrics on an infinite set.

How to cite

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Qiu, Dong, and Zhang, Weiquan. "The strongest t-norm for fuzzy metric spaces." Kybernetika 49.1 (2013): 141-148. <http://eudml.org/doc/252499>.

@article{Qiu2013,
abstract = {In this paper, we prove that for a given positive continuous t-norm there is a fuzzy metric space in the sense of George and Veeramani, for which the given t-norm is the strongest one. For the opposite problem, we obtain that there is a fuzzy metric space for which there is no strongest t-norm. As an application of the main results, it is shown that there are infinite non-isometric fuzzy metrics on an infinite set.},
author = {Qiu, Dong, Zhang, Weiquan},
journal = {Kybernetika},
keywords = {fuzzy metric space; t-norm; isometry; analysis; fuzzy metric space; t-norm; isometry; analysis; infinite non-isometric fuzzy metrics; infinite set},
language = {eng},
number = {1},
pages = {141-148},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The strongest t-norm for fuzzy metric spaces},
url = {http://eudml.org/doc/252499},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Qiu, Dong
AU - Zhang, Weiquan
TI - The strongest t-norm for fuzzy metric spaces
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 1
SP - 141
EP - 148
AB - In this paper, we prove that for a given positive continuous t-norm there is a fuzzy metric space in the sense of George and Veeramani, for which the given t-norm is the strongest one. For the opposite problem, we obtain that there is a fuzzy metric space for which there is no strongest t-norm. As an application of the main results, it is shown that there are infinite non-isometric fuzzy metrics on an infinite set.
LA - eng
KW - fuzzy metric space; t-norm; isometry; analysis; fuzzy metric space; t-norm; isometry; analysis; infinite non-isometric fuzzy metrics; infinite set
UR - http://eudml.org/doc/252499
ER -

References

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  2. George, A., Veeramani, P., 10.1016/0165-0114(94)90162-7, Fuzzy Set and Systems 64 (1994), 395-399. Zbl0843.54014MR1289545DOI10.1016/0165-0114(94)90162-7
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  4. Gregori, V., Morillas, S., Sapena, A., Examples of fuzzy metrics and applications., Fuzzy Set and Systems 170 (2011), 95-111. Zbl1210.94016MR2775611
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  7. Menger, K., 10.1073/pnas.28.12.535, Proc. Nat. Acad. Sci. USA 28 (1942), 535-537. Zbl0063.03886MR0007576DOI10.1073/pnas.28.12.535
  8. Sapena, A., A contribution to the study of fuzzy metric spaces., Appl. Gen. Topology 2 (2001), 63-76. Zbl1249.76040MR1863833
  9. Schweizer, B., Sklar, A., Statistical metric spaces., Pacific J. Math. 10 (1960), 314-334. Zbl0136.39301MR0115153
  10. Schweizer, B., Sklar, A., Probabilistic Metric Spaces., North Holland, Amsterdam 1983. Zbl0546.60010MR0790314
  11. Thorp, E., 10.1090/S0002-9939-1960-0119302-6, Proc. Amer. Math. Soc. 11 (1960), 734-740. Zbl0125.37002MR0119302DOI10.1090/S0002-9939-1960-0119302-6

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