In finite sets with n elements, every similarity relation (or fuzzy equivalence) can be represented by an n x n-matrix S = (sij), sij ∈ [0,1], such that sii = 1 (1 ≤ i ≤ n), sij = sji for any i,j and S o S = S, where o denotes the max-min product of matrices. These matrices represent also dendograms and sets of closed balls of a finite ultrametric space (vid. [1], [2], [3]).
@article{urn:eudml:doc:39849,
title = {How similarity matrices are?},
journal = {Stochastica},
volume = {2},
year = {1978},
pages = {77-80},
zbl = {0418.94033},
mrnumber = {MR0562436},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39849}
}
Riera, Teresa. How similarity matrices are?. Stochastica, Tome 2 (1978) pp. 77-80. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39849/