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

ƒ-inclusion indexes between fuzzy sets

Authors
Nicolás Madrid, Manuel Ojeda-Aciego, Irina Perfilieva
Corresponding Author
Nicolás Madrid
Available Online June 2015.
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.217How to use a DOI?
Keywords
f-inclusion, index of subsethood, fuzzy sets.
Abstract

We introduce the notion of f-inclusion, which is used to describe different kinds of subsethood relations between fuzzy sets by means of monotonic functions ƒ: [0, 1] [0, 1]. We show that these monotonic functions can be considered indexes of inclusion, since the greater the function considered, the more restrictive is the relationship. Finally, we propose a general index of inclusion by proving the existence of a representative f-inclusion for any two ordered pairs of fuzzy sets. In such a way, our approach is different from others in the literature in no taking a priori assumptions like residuated implications or t-norms.

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-15.2015.217How 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  - Nicolás Madrid
AU  - Manuel Ojeda-Aciego
AU  - Irina Perfilieva
PY  - 2015/06
DA  - 2015/06
TI  - ƒ-inclusion indexes between fuzzy sets
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  - 1528
EP  - 1533
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.217
DO  - https://doi.org/10.2991/ifsa-eusflat-15.2015.217
ID  - Madrid2015/06
ER  -