On efficient factorization of standard fuzzy concept lattices and attribute-oriented fuzzy concept lattices
We propose two ways to make factorization of attribute-oriented fuzzy concept lattices recently studied by Ciobanu & Văideanu more efficient. Firstly, we show that the blocks of the corresponding factor lattice are determined by a particular fuzzy interior operator. This allows us to compute an...
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| Vydané v: | Fuzzy sets and systems Ročník 351; s. 108 - 121 |
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| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier B.V
15.11.2018
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| ISSN: | 0165-0114, 1872-6801 |
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| Abstract | We propose two ways to make factorization of attribute-oriented fuzzy concept lattices recently studied by Ciobanu & Văideanu more efficient. Firstly, we show that the blocks of the corresponding factor lattice are determined by a particular fuzzy interior operator. This allows us to compute an attribute-oriented fuzzy concept lattice by intents. Such a computation requires fewer traversals through data, as the number of the attributes is usually smaller than the number of objects. Secondly, we scale the input data in such a way that the factor lattice can be computed as a one-sided fuzzy-crisp concept lattice. Our experiments indicate that both methods lead to a significant improvement in efficiency of computation of the factor lattice. In addition, we improve and extend the theory provided by Ciobanu & Văideanu. |
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| AbstractList | We propose two ways to make factorization of attribute-oriented fuzzy concept lattices recently studied by Ciobanu & Văideanu more efficient. Firstly, we show that the blocks of the corresponding factor lattice are determined by a particular fuzzy interior operator. This allows us to compute an attribute-oriented fuzzy concept lattice by intents. Such a computation requires fewer traversals through data, as the number of the attributes is usually smaller than the number of objects. Secondly, we scale the input data in such a way that the factor lattice can be computed as a one-sided fuzzy-crisp concept lattice. Our experiments indicate that both methods lead to a significant improvement in efficiency of computation of the factor lattice. In addition, we improve and extend the theory provided by Ciobanu & Văideanu. |
| Author | Konecny, Jan |
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| Cites_doi | 10.1016/j.eswa.2015.04.044 10.1016/j.ins.2012.02.064 10.1016/j.fss.2016.07.004 10.1016/j.ins.2010.11.011 10.1016/j.ins.2014.10.011 10.1093/jigpal/jzi045 10.1007/s10472-010-9199-5 10.1080/03081079.2013.862377 10.1080/03081079.2012.685936 10.1016/j.jcss.2007.03.016 10.1090/S0002-9947-1939-1501995-3 10.1016/j.ijar.2016.02.004 10.1016/j.ins.2011.09.023 |
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| References | Krajca, Outrata, Vychodil (br0160) 2010; 59 Andrews (br0010) 2015; 295 Ganter, Wille (br0110) 1999 Ward, Dilworth (br0210) 1939; 45 Ciobanu, Văideanu (br0080) 2017; 317 Belohlavek, Krmelova (br0060) 2013 Konecny, Krupka (br0150) 2016; 73 Belohlavek, Vychodil (br0070) 2012; 41 Konecny (br0140) 2011; 181 Belohlavek, Dvořák, Outrata (br0040) 2007; 73 Dias, Vieira (br0100) 2015; 42 Hájek (br0130) November 2001 Belohlavek, Konecny (br0050) 2012; 199 Czédli (br0090) 1982; 44 Outrata, Vychodil (br0190) 2012; 185 Belohlavek (br0020) 2002 Kuznetsov (br0180) 1993 Ben Yahia, Jaoua (br0220) 2001 Belohlavek (br0030) 2002 Poelmans, Ignatov, Kuznetsov, Dedene (br0200) 2014; 43 Ganter, Kuznetsov (br0120) 2001 Krajci (br0170) 2005; 13 Dias (10.1016/j.fss.2018.01.012_br0100) 2015; 42 Hájek (10.1016/j.fss.2018.01.012_br0130) 2001 Poelmans (10.1016/j.fss.2018.01.012_br0200) 2014; 43 Kuznetsov (10.1016/j.fss.2018.01.012_br0180) 1993 Ganter (10.1016/j.fss.2018.01.012_br0120) 2001 Ward (10.1016/j.fss.2018.01.012_br0210) 1939; 45 Ben Yahia (10.1016/j.fss.2018.01.012_br0220) 2001 Konecny (10.1016/j.fss.2018.01.012_br0150) 2016; 73 Belohlavek (10.1016/j.fss.2018.01.012_br0040) 2007; 73 Ganter (10.1016/j.fss.2018.01.012_br0110) 1999 Krajca (10.1016/j.fss.2018.01.012_br0160) 2010; 59 Andrews (10.1016/j.fss.2018.01.012_br0010) 2015; 295 Belohlavek (10.1016/j.fss.2018.01.012_br0030) 2002 Belohlavek (10.1016/j.fss.2018.01.012_br0050) 2012; 199 Outrata (10.1016/j.fss.2018.01.012_br0190) 2012; 185 Belohlavek (10.1016/j.fss.2018.01.012_br0020) 2002 Ciobanu (10.1016/j.fss.2018.01.012_br0080) 2017; 317 Belohlavek (10.1016/j.fss.2018.01.012_br0060) 2013 Belohlavek (10.1016/j.fss.2018.01.012_br0070) 2012; 41 Konecny (10.1016/j.fss.2018.01.012_br0140) 2011; 181 Czédli (10.1016/j.fss.2018.01.012_br0090) 1982; 44 Krajci (10.1016/j.fss.2018.01.012_br0170) 2005; 13 |
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