Publication at Faculty of Arts |
2005
Abstract
In the framework of Henkin-style higher-order fuzzy logic we define two kinds of the fuzzy lattice completion. The fuzzy MacNeille completion is the lattice completion by (possibly fuzzy) stable sets; the fuzzy Dedekind completion is the lattice completion by (possibly fuzzy) Dedekind cuts.
We investigate the properties and interrelations of both notions and compare them to the results from the literature. Our attention is restricted to crisp dense linear orderings, which are important for the theory of fuzzy real numbers.