On fuzzy similarity relations
β Scribed by Tomasa Calvo
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 162 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0165-0114
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We show that for a fuzzy partial order R on a ΓΏnite universe , there is a ΓΏnite 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 ΓΏnite set is
A simple proof is given for the fact that the number of nonsingular similarity relations on (1,2,... n), for which the transitive closure consists of k blocks, equals ("\*;'\_i-') -(2"-fh -'), 1, =G k s n/2. In particular, this implies a recent result of Shapiro about Catalan numbers and Fine's Jequ
The notion of a transitive closure of a fuzzy relation is very useful for clustering in pattern recognition, for fuzzy databases, etc. It is based on translating the standard definition of transitivity and transitive closure into fuzzy terms. This definition works fine, but to some extent it does no