| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4943864 | Fuzzy Sets and Systems | 2017 | 24 Pages |
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 Åukasiewicz t-norm or to the product t-norm.
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Wei Li, Hongliang Lai, Dexue Zhang,