Abstract
Formal concept analysis (FCA) provides a theoretical framework for learning hierarchies of knowledge clusters. This paper is devoted to the study of the fuzzy concept in FCA. We propose a fuzzy relation on the universe to characterize the similarity of the objects. Based on fuzzy rough set model, we present a kind of approximation operators to characterize the fuzzy concept and its accuracy degree in FCA. The basic properties of these operators are investigated.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel, Dordrecht-Boston (1982)
Gediga, G., Wille, R.: Formal Concept Analysis-Mathematic Foundations. Springer, Berlin (1999)
Hu, K.Y., Lu, C.Y., Shi, C.Y.: Advances in concept lattice and its application. Journal of Tsinghua University (Science and Technology) 40(9), 77–81 (2000)
Ho, T.B.: An approach to concept formation based on formal concept analysis. IEICE Trans. Information and Systems E782D(5), 553–559 (1995)
Oosthuizen, G.D.: The application of concept lattice to machine learning. Technical Report, University of Pretoria, South Africa (1996)
Zhang, W.X., Wei, L., Qi, J.J.: Attribute reduction theory and approach to concept lattice. Science in China, Ser. F Information Sciences 6(48), 713–726 (2005)
Godin, R.: Incremental concept formation algorithm based on Galois (concept) lattices. Computational Intelligence 11(2), 246–267 (1995)
Yao, Y.Y.: Concept lattices in rough set theory. In: Dick, S., Kurgan, L., Pedrycz, W., et al. (eds.) Proceedings of 2004 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS 2004), pp. 796–801. IEEE Catalog Number: 04TH8736, June 27–30, 2004
Oosthuizen, G.D.: Rough sets and concept lattices. In: Ziarko, W.P. (ed.) Rough Sets, and Fuzzy Sets and Knowledge Discovery (RSKD93), pp. 24–31. Springer- Verlag, London (1994)
Zhang, X.H., Dai, J.H., Yu, Y.C.: On the union and intersection operations of rough sets based on various approximation spaces. Information Sciences 292, 214–229 (2015)
Zhang, X.H., Zhou, B., Li, P.: A general frame for intuitionistic fuzzy rough sets. Information Sciences 216, 34–49 (2012)
Tonella, P.: Using a concept lattice of decomposition slices for program understanding and impact analysis. IEEE Transactions on Software Engineering 29(6), 495–509 (2003)
Grigoriev, P.A., Yevtushenko, S.A.: Elements of an agile discovery environment. In: Grieser, G., Tanaka, Y., Yamamoto, A. (eds.) DS 2003. LNCS (LNAI), vol. 2843, pp. 311–319. Springer, Heidelberg (2003)
Yang, J.L., Qin, K.Y.: Uncertain concepts in a formal context. In: ICAMMS (2014)
Qin, K.Y., Meng, L.D.: Analysis on uncertain concepts of formal context. In: 2014 International Conference on Control Engineering and Automation (ICCEA 2014), pp. 315–319 (2015)
Ganter, B., Wille, R.: Formal Concept Analysis. Springer-Verlag, Heidelberg (1999)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)
Dubois, D., Prade, H.: Rough fuzzy set and fuzzy rough sets. International Journal of General Systems 17, 191–209 (1990)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Meng, L., Qin, K. (2015). Fuzzy Concepts in Formal Context. In: Tan, Y., Shi, Y., Buarque, F., Gelbukh, A., Das, S., Engelbrecht, A. (eds) Advances in Swarm and Computational Intelligence. ICSI 2015. Lecture Notes in Computer Science(), vol 9142. Springer, Cham. https://doi.org/10.1007/978-3-319-20469-7_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-20469-7_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-20468-0
Online ISBN: 978-3-319-20469-7
eBook Packages: Computer ScienceComputer Science (R0)