ƒ-inclusion indexes between fuzzy sets
Nicolás Madrid, Manuel Ojeda-Aciego, Irina Perfilieva
Available Online June 2015.
- 10.2991/ifsa-eusflat-15.2015.217How to use a DOI?
- f-inclusion, index of subsethood, fuzzy sets.
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.
- © 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 - 10.2991/ifsa-eusflat-15.2015.217 ID - Madrid2015/06 ER -