Lattice of partially ordered fuzzy subalgebras
✍ Scribed by Branimir Šešelja
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 364 KB
- Volume
- 81
- Category
- Article
- ISSN
- 0165-0114
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📜 SIMILAR VOLUMES
For any universal algebra, another universal algebra of the same type is constructed in such a way that there is a one-to-one correspondence between the fuzzy subalgebras of the former and certain crisp subalgebras of the latter.
We show that for a fuzzy partial order R on a ÿnite universe , there is a ÿnite family of fuzzy linear orders {Li: 16i6k} such that R(x; y) = min{ L i (x; y): 16i6k} for all x and y. This generalizes a well-known result on crisp partial orders, which states that each partial order on a ÿnite set is
## Behrendt, G., The lattice of antichain cutsets of a partially ordered set, Discrete Mathematics 89 (1991) 201-202. Every finite lattice is isomorphic to the lattice of antichain cutsets of a finite partially ordered set whose chains have at most three elements. A subset A of a partially order