Optimal decompositions of matrices with entries from residuated lattices

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F12%3A33147464" target="_blank" >RIV/61989592:15310/12:33147464 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1093/logcom/exr023" target="_blank" >http://dx.doi.org/10.1093/logcom/exr023</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/logcom/exr023" target="_blank" >10.1093/logcom/exr023</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Optimal decompositions of matrices with entries from residuated lattices

Popis výsledku v původním jazyce

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 x m object-attribute matrix I, we look for a decomposition of I into a product A * B of an n x k object-factor matrix A and a k x m factor-attribute matrix B with entries from L with the number k of factors as small as possible. We show that formal concepts of I, which play a central role in the Port-Royal approach to logic and which are the fixpoints of particular Galois connections associated to I, are optimal factors for decomposition of I in that they provide us with decompositions with the smallest number of factors. Moreover, we describe transformations between the space of original attributes and the space of factors induced by a decomposition I = A * B. The art

Název v anglickém jazyce

Optimal decompositions of matrices with entries from residuated lattices

Popis výsledku anglicky

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 x m object-attribute matrix I, we look for a decomposition of I into a product A * B of an n x k object-factor matrix A and a k x m factor-attribute matrix B with entries from L with the number k of factors as small as possible. We show that formal concepts of I, which play a central role in the Port-Royal approach to logic and which are the fixpoints of particular Galois connections associated to I, are optimal factors for decomposition of I in that they provide us with decompositions with the smallest number of factors. Moreover, we describe transformations between the space of original attributes and the space of factors induced by a decomposition I = A * B. The art

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP202%2F10%2F0262" target="_blank" >GAP202/10/0262: Rozklady matic s binárními a ordinálními daty: teorie, algoritmy, složitost</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2012

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Logic and Computation Advance Access

ISSN

0955-792X

e-ISSN

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Svazek periodika

22

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

21

Strana od-do

1405-1425

Kód UT WoS článku

000311670000007

EID výsledku v databázi Scopus

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