On lattice-ordered $t_{r}$-norms for type-2 fuzzy sets
General Mathematics
2020-04-09 v1
Abstract
In this paper, it is proved that, for the truth value algebra of interval-valued fuzzy sets, the distributive laws do not imply the monotonicity condition for the set inclusion operation. Then, a lattice-ordered -norm, which is not the convolution of -norms on , is obtained. These results negatively answer two open problems posed by Walker and Walker in [15].
Cite
@article{arxiv.2004.03593,
title = {On lattice-ordered $t_{r}$-norms for type-2 fuzzy sets},
author = {Xinxing Wu and Guanrong Chen},
journal= {arXiv preprint arXiv:2004.03593},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:2003.11953 and arXiv:1908.10532