Abstract
AFS (Axiomatic Fuzzy Sets) -based formal concept is a generalization and development of classical concept lattice and monotone concept, which can be applied to represent the logic operations of queries in information retrieval. Granular computing is an emerging field of study that attempts to formalize and explore methods and heuristics of human problem solving with multiple levels of granularity and abstraction. The main objective of this paper is to investigate and develop AFS-based formal concept by using granule logics. Some generalized formulas of granular computing are introduced, in which AFS-based formal concept and AFS-based formal concept on multi-valued context are interpreted from the point of granular computing, respectively.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bargiela, A., Pedrycz, W.: Granular Computing: An Introduction. Kluwer Academic Publishers, Boston (2002)
Deogun, J.S., Saquer, J.: Monotone Concepts for Formal Concept Analysis. Discrete Appl. Math. 144, 70–78 (2004)
Hirota, K., Pedrycz, W.: Fuzzy Computing for Data Mining. Proc. of the IEEE 87, 1575–1600 (1999)
Lin, T.Y.: Granular Computing. Announcement of the BISC Special Interest Group on Granular Computing (1997)
Lin, T.Y.: Granular Computing, Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 16–24. Springer, Heidelberg (2003)
Liu, X.D.: The Fuzzy Theory Based on AFS Algebras and AFS Structure. J. Math. Anal. Appl. 217, 459–478 (1998)
Liu, X.D., Pedrycz, W.: Axiomatic Fuzzy Set Theroy and Its Applications. Springer, Heidelberg (2009)
Pawlak, Z.: Rough Sets-Theoretical Aspects of Reasoning About Data. Kluwer Publishers, Boston (1991)
Pedrycz, W.: Granular Computing: An Emerging Paradigm. Physica-Verlag, Heidelberg (2001)
Qiu, G.F., Ma, J.M., Yang, H.Z., Zhang, W.X.: A Mathematical Model for Concept Granular Computing Systems. Sci China Inf. Sci. 53(7), 1397–1408 (2010)
Wang, L.D., Liu, X.D.: Concept Analysis via Rough Set and AFS Algebra. Inf. Sci. 178(21), 4125–4137 (2008)
Wang, L.D., Liu, X.D., Qiu, W.R.: Nearness Approximation Space Based on Axiomatic Fuzzy Sets. Int. J. Approx. Reason 53, 200–211 (2012)
Wei, L., Zhang, X.H., Qi, J.J.: Granular Reduction of Property-Oriented Concept Lattices. In: Croitoru, M., Ferré, S., Lukose, D. (eds.) ICCS 2010. LNCS, vol. 6208, pp. 154–164. Springer, Heidelberg (2010)
Wille, R.: Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel (1982)
Wu, W.Z., Leung, Y., Mi, J.S.: Granular Computing and Knowledge Reduction in Formal Contexts. IEEE T Knwl. Data En. 21(10), 1461–1474 (2009)
Yao, J.T.: A Ten-Year Review of Granular Computing. In: GrC 2007, pp. 734–739 (2007)
Yao, Y.Y.: Granular Computing: Basic Issues and Possible Solutions. In: Proceedings of the 5th Joint Conference on Information Sciences, pp. 186–189 (2000)
Yao, Y.Y.: A Partition Model of Granular Computing. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 232–253. Springer, Heidelberg (2004)
Yao, Y.Y., Zhou, B.: A Logic Language of Granular Computing. In: 6th IEEE International Conference on Cognitive Informatics, pp. 178–185 (2007)
Zadeh, L.A.: Fuzzy Sets and Information Granurity. In: Gupta, M., Ragade, R.K., Yager, R.R. (eds.) Advances in Fuzzy Set Theory and Applications, pp. 3–18. North-Holland Publishing Company (1979)
Zadeh, L.A.: Key Roles of Information Granulation and Fuzzy Logic in Human Reasoning, Concept Formulation and Computing with Words. In: Proceedings of IEEE 5th International Fuzzy Systems, p. 1 (1996)
Zadeh, L.A.: Towards a Theory of Fuzzy Information Granulation and Its Centrality in Human Reasoning and Fuzzy Logic. Fuzzy Set Syst. 90(2), 111–127 (1997)
Zadeh, L.A.: Some Reflections on Soft Computing, Granular Computing and their Roles in the Conception, Design And Utilization of Information/Intelligent Systems. Soft Comput. 2, 23–25 (1998)
Zhao, Y., Halang, W.A., Wang, X.: Rough Ontology Mapping in E-Business Integration. SCI, vol. 37, pp. 75–93. Springer, Heidelberg (2007)
Zhou, B., Yao, Y.Y.: A Logic Approach to Granular Computing. Int. J. Cogn. Inform. Natl. Intell. 2, 63–79 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, L., Liu, X., Wang, X. (2012). AFS-Based Formal Concept Analysis within the Logic Description of Granules. 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_38
Download citation
DOI: https://doi.org/10.1007/978-3-642-32115-3_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32114-6
Online ISBN: 978-3-642-32115-3
eBook Packages: Computer ScienceComputer Science (R0)