Ordinal sum of two binary operations being a t-norm on bounded lattice
General Mathematics
2023-01-19 v2
Abstract
The ordinal sum of t-norms on a bounded lattice has been used to construct other t-norms. However, an ordinal sum of binary operations (not necessarily t-norms) defined on the fixed subintervals of a bounded lattice may not be a t-norm. Some necessary and sufficient conditions are presented in this paper for ensuring that an ordinal sum on a bounded lattice of two binary operations is, in fact, a t-norm. In particular, the results presented here provide an answer to an open problem put forward by Ertu\u{g}rul and Ye\c{s}ilyurt [Ordinal sums of triangular norms on bounded lattices, Inf. Sci., 517 (2020) 198-216].
Cite
@article{arxiv.2003.03013,
title = {Ordinal sum of two binary operations being a t-norm on bounded lattice},
author = {Xinxing Wu and Qin Zhang and Xu Zhang and Gül Deniz Çaylı and Lidong Wang},
journal= {arXiv preprint arXiv:2003.03013},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:1907.06638 by other authors