Abstract
Knowledge reduction is one of the key issues in real formal concept analysis. This study investigates the issue of developing efficient knowledge reduction methods for real decision formal contexts. A corresponding heuristic algorithm is proposed and some numerical experiments are conducted to assess its efficiency.
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References
Aswani-Kumar, C., Srinivas, S.: Concept lattice reduction using fuzzy K-Means clustering. Expert Systems with Applications 37(3), 2696–2704 (2010)
Bĕlohlávek, R.: Fuzzy Galois connections. Mathematical Logic Quarterly 45(4), 497–504 (1999)
Burusco, A., Fuentes-González, R.: The study of the L-fuzzy concept lattice. Mathware and Soft Computing 3, 209–218 (1994)
Düntsch, I., Gediga, G.: Approximation Operators in Qualitative Data Analysis. In: de Swart, H., Orłowska, E., Schmidt, G., Roubens, M. (eds.) TARSKI 2003. LNCS, vol. 2929, pp. 214–230. Springer, Heidelberg (2003)
Elloumi, S., Jaam, J., Hasnah, A., Jaoua, A., Nafkha, I.: A multi-level conceptual data reduction approach based on the Lukasiewicz implication. Information Sciences 163(4), 253–262 (2004)
Ganter, B., Wille, R.: Formal Concept Analysis, Mathematical Foundations. Springer, Berlin (1999)
Jaoua, A., Elloumi, S.: Galois connection, formal concepts and Galois lattice in real relations: application in a real classifier. The Journal of Systems and Software 60, 149–163 (2002)
Li, J., Mei, C., Lv, Y.: Knowledge reduction in decision formal contexts. Knowledge-Based Systems 24(5), 709–715 (2011)
Li, J., Mei, C., Lv, Y.: A heuristic knowledge-reduction method for decision formal contexts. Computers and Mathematics with Applications 61(4), 1096–1106 (2011)
Li, J., Mei, C., Lv, Y.: Knowledge reduction in formal decision contexts based on an order-preserving mapping. International Journal of General Systems 41(2), 143–161 (2012)
Li, J., Mei, C., Lv, Y.: Knowledge reduction in real decision formal contexts. Information Sciences 189, 191–207 (2012)
Li, L.F., Zhang, J.K.: Attribute reduction in fuzzy concept lattices based on T implication. Knowledge-Based Systems 23(6), 497–503 (2010)
Liu, M., Shao, M.W., Zhang, W.X., Wu, C.: Reduction method for concept lattices based on rough set theory and its application. Computers and Mathematics with Applications 53(9), 1390–1410 (2007)
Mi, J.S., Leung, Y., Wu, W.Z.: Approaches to attribute reduction in concept lattices induced by axialities. Knowledge-Based Systems 23(6), 504–511 (2010)
Pei, D., Li, M.Z., Mi, J.S.: Attribute reduction in fuzzy decision formal contexts. In: 2011 International Conference on Machine Learning and Cybernetics, pp. 204–208. IEEE Press, New York (2011)
Popescu, A.: A general approach to fuzzy concepts. Mathematical Logic Quarterly 50(3), 265–280 (2004)
Wang, H., Zhang, W.X.: Approaches to knowledge reduction in generalized consistent decision formal context. Mathematical and Computer Modelling 48(11-12), 1677–1684 (2008)
Wei, L., Qi, J.J., Zhang, W.X.: Attribute reduction theory of concept lattice based on decision formal contexts. Science in China: Series F—Information Sciences 51(7), 910–923 (2008)
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 Transactions on Knowledge and Data Engineering 21(10), 1461–1474 (2009)
Yang, H.Z., Leung, Y., Shao, M.W.: Rule acquisition and attribute reduction in real decision formal contexts. Soft Computing 15(6), 1115–1128 (2011)
Yao, Y.Y.: Concept lattices in rough set theory. In: Dick, S., Kurgan, L., Pedrycz, W., Reformat, M. (eds.) Proceedings of 23rd International Meeting of the North American Fuzzy Information Processing Society, pp. 796–801. IEEE Press, New York (2004)
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., Ma, J.M., Fan, S.Q.: Variable threshold concept lattices. Information Sciences 177(22), 4883–4892 (2007)
Zhang, W.X., Qiu, G.F.: Uncertain decision making based on rough sets. Tsinghua University Press, Beijing (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)
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Li, J., Mei, C., Lv, Y., Zhang, X. (2012). A Heuristic Knowledge Reduction Algorithm for Real Decision Formal Contexts. In: Yao, J., et al. Rough Sets and Current Trends in Computing. RSCTC 2012. Lecture Notes in Computer Science(), vol 7413. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32115-3_36
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DOI: https://doi.org/10.1007/978-3-642-32115-3_36
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