Yoneda completeness and flat completeness of ordered fuzzy sets
Abstract
This paper studies Yoneda completeness and flat completeness of ordered fuzzy sets valued in the quantale obtained by endowing the unit interval with a continuous triangular norm. Both of these notions are natural extension of directed completeness in order theory to the fuzzy setting. Yoneda completeness requires every forward Cauchy net converges (has a Yoneda limit), while flat completeness requires every flat weight (a counterpart of ideals in partially ordered sets) has a supremum. It is proved that flat completeness implies Yoneda completeness, but, the converse implication holds only in the case that the related triangular norm is either isomorphic to the Lukasiewicz t-norm or to the product t-norm.
Cite
@article{arxiv.1607.03212,
title = {Yoneda completeness and flat completeness of ordered fuzzy sets},
author = {Wei Li and Hongliang Lai and Dexue Zhang},
journal= {arXiv preprint arXiv:1607.03212},
year = {2016}
}
Comments
25 pages in Fuzzy Sets and Systems (2016)