Abstract
Attribute reduction in concept lattices is one of the key problems in the study of concept lattice theory. This paper defines a homomorphism consistent set and provides an approach to attribute reduction of a consistent decision formal context based on concept lattices. We also examine the relationship between homomorphism consistent set and attribute consistent set. The method for judging a homomorphism consistent set is simpler than the existing ones.
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Wille R (1982) Restructuring lattice theory: approach based on hierarchies of concepts. In: Rival I (ed) Ordered sets. Reidel, Dordrecht-Boston, pp 445–470
Zhang W-X, Qiu G-F (2005) Uncertain decision making based on rough sets. Tsinghua University Press, Beijing
Ganter R, Wille B (1999) Formal concept analysis: mathematical foundations. Springer, Berlin
Ma J-M, Zhang W-X, Cai S (2006) Variable threshold concept lattice and dependence space. In Conference on Fuzzy systems and knowledge discovery, pp 109–118
Wang H, Zhang W-X (2008) Approaches to knowledge reduction in generalized consistent decision formal context. Math Comput Model 48:1677–1684
Carpineto C, Romano G (1993) Galois: an order-theoretic approach to conceptual clustering. In: Utgoff P (ed) Proceedings of ICML, vol 293. Elsevier, Amherst, pp 33–40
Duntsch I, Gediga G (2003) Approximation operators in qualitative data analysis. Lecture Notes in Computer Science, vol 2929. Springer, Berlin, pp 214–230
Godin R (1995) Incremental concept formation algorithm based on Galois (concept) lattice. Comput Intell 11:246–267
Wolff KE (2001) A conceptual view of knowledge bases in rough set theory. In: Rough sets and current trends in computing, Lecture Notes in Computer Science, vol 2005. Springer, Berlin, pp 220–228
Wang Y, Wang G-Y, Deng W-B (2007) Concept lattice based data-driven uncertain knowledge acquisition. Pattern Recogn Artif Intell 20(5)
Wei L, Qi J-J, Zhang W-X (2008) Attribute reduction in concept lattices of decision formal context. Sci China 38(2):195–208
Wang X, Zhang W-X (2008) Attribute reduction in concept lattices and attribute characteristics. Comput Eng Appl 44(12):1–4
Mi J-S, Leung Y, Wu W-Z (2010) Approaches to attribute reduction in concept lattices induced by axialities. Knowl Based Syst 23:504–511
Yao Y-Y (2004) Concept lattices in rough set theory. Fuzzy Inform 2:796–801
Acknowledgments
This paper is supported by the National Natural Science Foundation of China (No. 60963006, 61005042/F030502), and by Research Fund for the Doctoral Program of Higher Education of China 20101303110004.
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Pei, D., Mi, JS. Attribute reduction in decision formal context based on homomorphism. Int. J. Mach. Learn. & Cyber. 2, 289–293 (2011). https://doi.org/10.1007/s13042-011-0034-z
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DOI: https://doi.org/10.1007/s13042-011-0034-z