Abstract
Konwledge reduction on concept lattices is an important research topic in formal concept analysis, and there are some different meanings and methods. This paper mainly studies the granular reduction of property-oriented concept lattices which can preserve the property-oriented concepts, which is called granules in this paper. Firstly, the granules of a property-oriented concept lattice is presented, and it is proven that each extension of property-oriented concepts can be constructed by the granules. Then, the granular reduction of a property-oriented concept lattice is proposed, and the granular discernibility attribute matrix and the granular discernibility attribute function are respectively employed to determine granular consistent sets and calculate granular reducts. Finally, the relation between a granular consistent set and a lattice consistent set of a property-oriented concept lattice is discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chen, Y.H., Yao, Y.Y.: A multiview approach for intelligent data analysis based on data operators. Information Sciences 178(1), 1–20 (2008)
Duntsch, I., Gediga, G.: Approximation operators in qualitative data analysis. In: de Swart, H., Orlowska, E., Schmidt, G., Roubens, M. (eds.) Theory and Application of Relation of Structures as Knowledge Instruments, pp. 216–233. Springer, Heidelberg (2003)
Ganter, B., Wille, R.: Formal Concept Analysis, Mathematical Foundations. Springer, Berlin (1999)
Gediga, G., Duntsch, I.: Modal-style operations in qualitative data analysis. In: Proceedings of the 2002 IEEE International Conference on Data Mining, pp. 155–162 (2002)
Gély, A., Medina, R., Nourine, L.: Representing lattices using many-valued relations. Information Sciences 179, 2729–2739 (2009)
Godin, R., Missaoui, R., Alaoui, H.: Incremental Concept Formation Algorithms Based on Galois (Concept) Lattices. Computational Intelligence 11(2), 246–267 (1995)
Kent, R.E., Bowman, C.M.: Digital libraries, conceptual knowledge systems and the nebula interface. Technical Report, University of Arkansas (1995)
Liu, M.Q., Wei, L., Zhao, W.: The reduction theory of object oriented concept lattices and property oriented concept lattices. In: Wen, P., et al. (eds.) RSKT 2009. LNCS, vol. 5589, pp. 587–593. Springer, Heidelberg (2009)
Sutton, A., Maletic, J.I.: Recovering UML class models from C++: A detailed explanation. Information and Software Technology 49(3), 212–229 (2007)
Wang, X., Ma, J.M.: A novel approach to attribute reduction in concept lattices. In: Wang, G.-Y., Peters, J.F., Skowron, A., Yao, Y. (eds.) RSKT 2006. LNCS (LNAI), vol. 4062, pp. 522–529. Springer, Heidelberg (2006)
Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel, Dordrecht (1982)
Wu, W.Z., Leung, Y., Mi, J.S.: Granular computing and knowledge reduction in formal contexts. IEEE Transaction on Knowledge and Data Engineering 21(10), 1464–1474 (2009)
Yao, Y.Y.: Concept lattices in rough set theory. In: Dick, S., Kurgan, L., Pedrycz, W., Reformat, M. (eds.) Proceedings of 2004 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS 2004), June 27-30, pp. 796–801 (2004), IEEE Catalog Number: 04TH8736
Yao, Y.Y.: A comparative study of formal concept analysis and rough set theory in data analysis. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 59–68. Springer, Heidelberg (2004)
Zhang, W.X., Wei, L., Qi, J.J.: Attribute reduction in concept lattice based on discernibility matrix. In: Ślęzak, D., Yao, J., Peters, J.F., Ziarko, W.P., Hu, X. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3642, pp. 157–165. Springer, Heidelberg (2005)
Zhang, W.X., Wei, L., Qi, J.J.: Attribute reduction theory and approach to concept lattice. Science in China Series F: Information Sciences 48(6), 713–726 (2005)
Zhang, W.X., Wang, X.: Relations of attribute reduction between object and property oriented lattices. Knowledge-Based Systems 21, 398–403 (2008)
Zhu, W.: Relationship between generalized rough sets based on binary relation and covering. Information Sciences 179, 210–225 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wei, L., Zhang, XH., Qi, JJ. (2010). Granular Reduction of Property-Oriented Concept Lattices. In: Croitoru, M., Ferré, S., Lukose, D. (eds) Conceptual Structures: From Information to Intelligence. ICCS 2010. Lecture Notes in Computer Science(), vol 6208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14197-3_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-14197-3_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14196-6
Online ISBN: 978-3-642-14197-3
eBook Packages: Computer ScienceComputer Science (R0)