Abstract
We introduce the notion of f-inclusion, which is used todescribe different kinds of subsethood relations betweenfuzzy sets by means of monotonic functions f: [0,1] →[0,1]. We show that these monotonic functions can beconsidered indexes of inclusion, since the greater thefunction considered, the more restrictive is the relation-ship. Finally, we propose a general index of inclusion byproving the existence of a representative f-inclusion forany two ordered pairs of fuzzy sets. In such a way, ourapproach is different from others in the literature in notaking a priori assumptions like residuated implicationsor t-norms.
Citation
Please, cite this work as:
[MOP15] N. Madrid, M. Ojeda-Aciego, and I. Perfilieva. “( f)-inclusion indexes between fuzzy sets”. In: 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (IFSA-EUSFLAT-15), Gijón, Spain., June 30, 2015. Ed. by J. M. Alonso, H. Bustince and M. Z. Reformat. Atlantis Press, 2015.
@InProceedings{Madrid2015,
author = {Nicol{’a}s Madrid and Manuel Ojeda-Aciego and Irina Perfilieva},
booktitle = {2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (IFSA-EUSFLAT-15), Gij{'{o}}n, Spain., June 30, 2015},
title = {{(f)}-inclusion indexes between fuzzy sets},
year = {2015},
editor = {Jos{’e} Maria Alonso and Humberto Bustince and Marek Z. Reformat},
publisher = {Atlantis Press},
abstract = {We introduce the notion of f-inclusion, which is used todescribe different kinds of subsethood relations betweenfuzzy sets by means of monotonic functions f: [0,1] →[0,1]. We show that these monotonic functions can beconsidered indexes of inclusion, since the greater thefunction considered, the more restrictive is the relation-ship. Finally, we propose a general index of inclusion byproving the existence of a representative f-inclusion forany two ordered pairs of fuzzy sets. In such a way, ourapproach is different from others in the literature in notaking a priori assumptions like residuated implicationsor t-norms.},
bibsource = {dblp computer science bibliography, https://dblp.org},
biburl = {https://dblp.org/rec/conf/eusflat/MadridOP15.bib},
timestamp = {Thu, 06 Oct 2022 12:30:16 +0200},
}