Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology

Generalized Distance and an Example of Fuzzy Metric

Authors
Fagner Santana, Fabiana Santana, Regivan Santiago
Corresponding Author
Fagner Santana
Available Online June 2015.
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.198How to use a DOI?
Keywords
i-Metric, fuzzy metric, topology, metrizability.
Abstract

In this paper we introduce a new notion of generalized metric, called i-metric. This generalization is made by changing the valuation space of the distance function. The result is an interesting distance function for the set of fuzzy numbers of Interval Type with non negative fuzzy numbers as values. This example of i-metric generates a topology in a very natural way, based on open balls. We prove that this topology is Hausdorff, regular but not metrizable (generated by an usual metric).

Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
Series
Advances in Intelligent Systems Research
Publication Date
June 2015
ISBN
978-94-62520-77-6
ISSN
1951-6851
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.198How to use a DOI?
Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Fagner Santana
AU  - Fabiana Santana
AU  - Regivan Santiago
PY  - 2015/06
DA  - 2015/06
TI  - Generalized Distance and an Example of Fuzzy Metric
BT  - Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
PB  - Atlantis Press
SP  - 1401
EP  - 1406
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.198
DO  - https://doi.org/10.2991/ifsa-eusflat-15.2015.198
ID  - Santana2015/06
ER  -