ƒ-inclusion indexes between fuzzy sets

DOI

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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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  - 10.2991/ifsa-eusflat-15.2015.217
ID  - Madrid2015/06
ER  -