×

On equivalence of conceptual scaling and generalized one-sided concept lattices. (English) Zbl 1328.68217

Summary: The methods of conceptual scaling and generalized one-sided concept lattices represent different possibilities on how to deal with many-valued contexts. We briefly describe these methods and prove that they are equivalent. In particular, we show that the application of these two approaches to a given many-valued context yields the same closure system on the set of all objects. Based on this equivalence, we propose a possible attribute reduction of one-sided formal contexts.

MSC:

68T30 Knowledge representation
06A15 Galois correspondences, closure operators (in relation to ordered sets)
06B23 Complete lattices, completions
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] L. Antoni, S. Krajči, O. Krídlo, B. Macek, L. Pisková, Relationship between two FCA approaches on heterogeneous formal contexts, in: In the 9th International Conference on Concept Lattices and Their Applications (CLA 2012), 2012, pp. 93-102.
[2] Bělohlávek, R., Lattices generated by binary fuzzy relations, Tatra Mt. Math. Publ., 16, 11-19, (1999) · Zbl 0949.06002
[3] Bělohlávek, R., Lattices of fixed points of fuzzy Galois connections, Math. Logic Quart., 47, 1, 111-116, (2001) · Zbl 0976.03025
[4] Bělohlávek, R., Fuzzy Galois connections, Math. Logic Quart., 45, 4, 497-504, (1999) · Zbl 0938.03079
[5] Bělohlávek, R., Concept lattices and order in fuzzy logic, Ann. Pure Appl. Logic, 128, 277-298, (2004) · Zbl 1060.03040
[6] R. Be lohlávek, What is a fuzzy concept lattice? II, in: Lecture Notes in Artificial Intelligence, vol. 6743, 2011, pp. 19-26.
[7] Bělohlávek, R.; Vychodil, V., What is a fuzzy concept lattice?, Proc. CLA, 2005, 34-45, (2005)
[8] Bělohlávek, R.; Vychodil, V., Formal concept analysis and linguistic hedges, Int. J. Gen. Syst., 41, 5, 503-532, (2012) · Zbl 1277.93045
[9] Ben Yahia, S.; Jaoua, A., Discovering knowledge from fuzzy concept lattice, (Kandel, A.; Last, M.; Bunke, H., Data Mining and Computational Intelligence, (2001), Physica-Verlag), 167-190
[10] Butka, P.; Pócs, J., Generalization of one-sided concept lattices, Comput. Inform., 32, 2, 355-370, (2013) · Zbl 1413.06008
[11] Ganter, B.; Wille, R., Formal Concept Analysis. Mathematical Foundations, (1999), Springer Berlin
[12] Georgescu, G.; Popescu, A., Concept lattices and similarity in non-commutative fuzzy logic, Fundam. Inform., 55, 1, 23-54, (2002) · Zbl 1023.03016
[13] Georgescu, G.; Popescu, A., Non-commutative fuzzy Galois connections, Soft Comput., 7, 458-467, (2003) · Zbl 1024.03025
[14] Georgescu, G.; Popescu, A., Non-dual fuzzy connections, Arch. Math. Logic, 43, 1009-1039, (2004) · Zbl 1060.03042
[15] Grätzer, G., Lattice theory: foundation, (2011), Springer Basel · Zbl 1233.06001
[16] Jaoua, A.; Elloumi, S., Galois connection formal concepts and Galois lattice in real relations: application in a real classifier, J. Syst. Softw., 60, 149-163, (2002)
[17] Krajči, S., Cluster based efficient generation of fuzzy concepts, Neural Netw. World, 13, 5, 521-530, (2003)
[18] Krajči, S., A generalized concept lattice, Logic J. IGPL, 13, 5, 543-550, (2005) · Zbl 1088.06005
[19] MacNeille, H. M., Partially ordered sets, Trans. Am. Math. Soc., 42, 416-460, (1937) · JFM 63.0833.04
[20] Markowsky, G., The factorization and representation of lattices, Trans. Am. Math. Soc., 203, 185-200, (1975) · Zbl 0302.06011
[21] Medina, J., Multi-adjoint property-oriented and object-oriented concept lattices, Inform. Sci., 190, 95-106, (2012) · Zbl 1248.68479
[22] Medina, J.; Ojeda-Aciego, M., Multi-adjoint t-concept lattices, Inform. Sci., 180, 5, 712-725, (2010) · Zbl 1187.68587
[23] Medina, J.; Ojeda-Aciego, M., On multi-adjoint concept lattices based on heterogeneous conjunctors, Fuzzy Sets Syst., 208, 95-110, (2012) · Zbl 1252.06003
[24] J. Medina, M. Ojeda-Aciego, J. Ruiz-Calviño, On multi-adjoint concept lattices: definition and representation theorem ICFCA 2007, in: Lecture Notes in Artificial Intelligence, 2007, pp. 197-209. · Zbl 1187.68588
[25] Medina, J.; Ojeda-Aciego, M.; Ruiz-Calviño, J., Formal concept analysis via multi-adjoint concept lattices, Fuzzy Sets Syst., 160, 130-144, (2009) · Zbl 1187.68589
[26] Ore, O., Galois connexions, Trans. Am. Math. Soc., 55, 493-513, (1944) · Zbl 0060.06204
[27] Pócs, J., Note on generating fuzzy concept lattices via Galois connections, Inform. Sci., 185, 1, 128-136, (2012) · Zbl 1239.68071
[28] Pócs, J., On possible generalization of fuzzy concept lattices using dually isomorphic retracts, Inform. Sci., 210, 89-98, (2012) · Zbl 1250.06001
[29] Pollandt, S., Fuzzy begriffe, (1997), Springer Verlag Berlin/Heidelberg · Zbl 0870.06008
[30] Popescu, A., A general approach to fuzzy concepts, Math. Logic Quart., 50, 3, 265-280, (2004) · Zbl 1059.03015
[31] Zhang, W. X.; Ma, J. M.; Fan, S. Q., Variable threshold concept lattices, Inform. Sci., 177, 22, 4883-4892, (2007) · Zbl 1130.06004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.