# Optimal decompositions of matrices with entries from residuated lattices

```@article{Belohlvek2012OptimalDO,
title={Optimal decompositions of matrices with entries from residuated lattices},
journal={J. Log. Comput.},
year={2012},
volume={22},
pages={1405-1425}
}```
• R. Belohlávek
• Published 1 December 2012
• Mathematics, Computer Science
• J. Log. Comput.
We describe optimal decompositions of matrices whose entries are elements of a residuated lattice L, such as L=[0, 1]. Such matrices represent relationships between objects and attributes with the entries representing degrees to which attributes represented by columns apply to objects represented by rows. Given such an n × m object-attribute matrix I, we look for a decomposition of I into a product A ° B of an n × k object-factor matrix A and a k × m factor-attribute matrix B with entries from…
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