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Generalizations of Approximable Concept Lattice

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Concept Lattices and Their Applications (CLA 2006)

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Abstract

B. Ganter, R. Wille initiated formal concept analysis. Concept lattice is one of the main notions and tools. Some researchers have investigated the fuzzification of the classical crisp concept lattice. One of them was shown by R. Bĕlohlávek : concept lattice in fuzzy setting. The second one was given by S. Kraj\(\check{c}\)i: generalized concept lattice. On the other hand, as a generalization of concept, Zhang, P. Hitzler, Shen defined the notion of approximable concept on a Chu space. In this paper, we introduce two generalizations of approximable concept lattice: approximable concept lattice in the sense of R. Bĕlohlávek, and generalized approximable concept in the sense of S. Kraj\(\check{c}\)i.

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References

  1. Bĕlohlávek, R.: Concept lattices and order in fuzzy logic. Annals of Pure and Applied Logic 128, 277–298 (2004)

    Article  MathSciNet  Google Scholar 

  2. Bĕlohlávek, R.: Fuzzy Galois connections. Math. Logic Quart. 45(4), 497–504 (1999)

    Google Scholar 

  3. Bĕlohlávek, R.: Fuzzy relational systems. In: Foundations and Principles. Foundations and Principles, Kluwer, New York (2002)

    Google Scholar 

  4. Bĕlohlávek, R., Sklena, V., Zacpal, J.: Crisply generated fuzzy concepts: reducing the number of concepts in formal concept analysis. In: Proc. 5th Int. Conf. on Recent Advances in Soft Computing, RASC 2004, Nottingham, United Kingdom, 16–18 December, 2004, pp. 524–529 (2004) pp. 63 (extended abstract) (full paper on the included CD)

    Google Scholar 

  5. Bĕlohlávek, R., Vychodil, V.: What is a fuzzy concept lattice? In: Proc. CLA 2005, 3rd Int. Conference on Concept Lattices and Their Applications, Olomouc, Czech Republic, pp. 34–45 (2005), http://sunsite.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-162/

  6. Bĕlohlávek, R., Vychodil, V.: Reducing the size of fuzzy concept lattices by hedges. In: FUZZ-IEEE 2005, The IEEE International Conference on Fuzzy Systems, Reno (Nevada, USA), May 22-25, 2005, pp. 663–668 (2005)

    Google Scholar 

  7. Ben Yahia, S., Jaoua, A.: Discovering knowledge from fuzzy concept lattice. In: Kandel, A., Last, M., Bunke, H. (eds.) Data Mining and Computational Intelligence, pp. 169–190. Physica-Verlag (2001)

    Google Scholar 

  8. Chen, X.Y., Li, Q.G.: Formal topology, Chu space and approximable concept. In: Proc. CLA, 3rd Int. Conference on Concept Lattices and Their Applications, Olomouc, Czech Republic, pp. 158–165 (2005), http://sunsite.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-162/

  9. Chen, X.Y., Li, Q.G., Deng, Z.K.: Chu space and approximable concept lattice in fuzzy setting. In: FUZZ-IEEE 2007, The IEEE International Conference on Fuzzy Systems, London, July 24-26 (2007)

    Google Scholar 

  10. Chen, X.Y.: Continuous lattice of L-sets (submitted)

    Google Scholar 

  11. Chen, X.Y., Li, Q.G., Deng, Z.K.: Way-below relation in fuzzy setting (Abstract). In: Proc. International Symposium on Domain Theory 2006, June 2-6, 2006, Hunan University, Changsha, P.R. China, pp. 22–25 (2006)

    Google Scholar 

  12. Chen, X.Y., Li, G.Q., Long, F., Deng, Z.K.: Generalizations of approximation concept lattice. In: Yahia, S.B., Nguifo, E.M. (eds.) Proceedings of CLA 2006: The 4th international conference on Concept Lattice and Their Applications, Yasmine Hammamet, Tunisia, October-November 2006, pp. 231–242 (2006)

    Google Scholar 

  13. Chen, X.Y.: Domain, Approximable Concept Lattice, Rough Sets and Topology, PhD thesis, Hunan University, P. R. China (2007)

    Google Scholar 

  14. Ganter, B., Wille, R.: Formal concept analysis. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  15. Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M., Scott, D.S.: A compendium of continuous lattices. Springer, Berlin Heidelberg, New York (1980)

    MATH  Google Scholar 

  16. Goguen, J.: L-fuzzy sets. J. Math. Anal. Appl. 18, 145–174 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  17. Hitzler, P., Zhang, G.Q.: A Cartesian Closed Category of Approximable Concept Structures. In: Wolff, K.E., Pfeiffer, H.D., Delugach, H.S. (eds.) ICCS 2004. LNCS (LNAI), vol. 3127, pp. 170–185. Springer, Heidelberg (2004)

    Google Scholar 

  18. Krajc̆i, S.: The basic theorem on generalized concept lattice. In Bĕlohlávek, V.R. (ed.) CLA 2004, Ostrava, Proceedings of the 2nd International Workshop, pp. 25-33(2004) ISBN 80-248-0597-9

    Google Scholar 

  19. Krajc̆i, S.: A generalized concept lattice. Logic Journal of IGPL 13(5) , 543–550 (2005 )

    Google Scholar 

  20. Krajči, S.: Cluster based efficient generation of fuzzy concepts. Neural Network World 13(5), 521–530 (2003)

    Google Scholar 

  21. Pratt, V.: Chu spaces as a semantic bridge between linear logic and mathematics. Theoretical Computer Science 294, 439–471 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  22. Vickers, S.: Topology via Logic. Cambridge Univ. Press, Cambridge (1989)

    MATH  Google Scholar 

  23. Zhang, G.Q., Shen, G.Q.: Approximable concepts, Chu spaces, and information systems. In: De Paiva, V., Pratt, V. (eds.) Theory and Applications of Categories Special Volume on Chu Spaces: Theory and Applications, vol. 17(5), pp. 80–102 (2006), http://newton.cwru.edu/publications.html

  24. Zhang, G.Q.: Chu space, concept lattices, and domains. Electronic Notes in Theoretical Computer Science 83, 17 (2004)

    Google Scholar 

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Sadok Ben Yahia Engelbert Mephu Nguifo Radim Belohlavek

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Chen, X., Li, Q., Long, F., Deng, Z. (2008). Generalizations of Approximable Concept Lattice. In: Yahia, S.B., Nguifo, E.M., Belohlavek, R. (eds) Concept Lattices and Their Applications. CLA 2006. Lecture Notes in Computer Science(), vol 4923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78921-5_7

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  • DOI: https://doi.org/10.1007/978-3-540-78921-5_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78920-8

  • Online ISBN: 978-3-540-78921-5

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