Paper:

# Fuzzy Concept Lattices Constrained by Hedges

## Radim Belohlavek^{*,**} and Vilem Vychodil^{**}

^{*}Dept. Systems Science and Industrial Engineering, T. J. Watson School of Engineering and Applied Science Binghamton University - SUNY, Binghamton, NY 13902-6000, USA

^{**}Dept. Computer Science, Palacky University, Olomouc, Tomkova 40, CZ-779 00 Olomouc, Czech Republic

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.11 No.6, pp. 536-545, 2007.

- [1] R. Belohlavek, “Fuzzy Galois connections,” Math. Logic Quarterly, 45, (4), pp. 497-504, 1999.
- [2] R. Belohlavek, “Reduction and a simple proof of characterization of fuzzy concept lattices,” Fundamenta Informaticae, 46, (4), pp. 277-285, 2001.
- [3] R. Belohlavek, “Fuzzy Relational Systems: Foundations and Principles,” Kluwer, Academic/Plenum Publishers, New York, 2002.
- [4] R. Belohlavek, “Concept lattices and order in fuzzy logic,” Ann. Pure Appl. Logic, 128, pp. 277-298, 2004.
- [5] R. Belohlavek and T. Funiokova, “Fuzzy interior operators,” Int. J. General Systems, 33, (4), pp. 315-330, 2004.
- [6] R. Belohlavek, T. Funioková, and V. Vychodil, “Galois connections with hedges,” In: Proc. 11th IFSA Congress 2005, pp. 1250-1255, Springer.
- [7] R. Belohlavek, V. Sklenar, and J. Zacpal, “Crisply Generated Fuzzy Concepts,” In: B. Ganter and R. Godin (Eds.), ICFCA 2005, LNCS, 3403, pp. 268-283, Springer-Verlag, Berlin/Heidelberg, 2005.
- [8] R. Belohlavek and V. Vychodil, “Reducing the size of fuzzy concept lattices by hedges,” In: FUZZ-IEEE 2005, The IEEE International Conference on Fuzzy Systems, May 22-25, 2005, Reno (Nevada, USA), pp. 663-668.
- [9] R. Belohlavek and V. Vychodil, “What is a fuzzy concept lattice?,” In: Proc. CLA 2005, 3rd Int. Conference on Concept Lattices and Their Applications, September 7-9, 2005, Olomouc, Czech Republic, pp. 34-45,

URL: http://ceur-ws.org/Vol-162/. - [10] R. Belohlavek and V. Vychodil, “Attribute implications in a fuzzy setting,” In: R. Missaoui and J. Schmid (Eds.), ICFCA 2006, LNAI, 3874, pp. 45-60, 2006.
- [11] S. B. Yahia and A. Jaoua, “Discovering knowledge from fuzzy concept lattice,” In: A. Kandel, M. Last, and H. Bunke, “Data Mining and Computational Intelligence,” pp. 167-190, Physica-Verlag, 2001.
- [12] A. Burusco and R. Fuentes-Gonzáles, “The study of the L-fuzzy concept lattice,” Mathware & Soft Computing, 3, pp. 209-218, 1994.
- [13] C. Carpineto and G. Romano, “Concept Data Analysis,” Theory and Applications, J. Wiley, 2004.
- [14] B. Ganter and R. Wille, “Formal Concept Analysis,” Mathematical Foundations, Springer, Berlin, 1999.
- [15] G. Gerla, “Fuzzy Logic,” Mathematical Tools for Approximate Reasoning, Kluwer, Dordrecht, 2001.
- [16] J. A. Goguen, “The logic of inexact concepts,” Synthese, 18, pp. 325-373, 1968-9.
- [17] P. Hájek, “Metamathematics of Fuzzy Logic,” Kluwer, Dordrecht, 1998.
- [18] P. Hájek, “On very true,” Fuzzy Sets and Systems, 124, pp. 329-333, 2001.
- [19] G. J. Klir and B. Yuan, “Fuzzy Sets and Fuzzy Logic,” Theory and Applications, Prentice Hall, 1995.
- [20] S. Krajči, “Cluster based efficient generation of fuzzy concepts,” Neural Network World, 5, pp. 521-530, 2003.
- [21] S. Krajči, “A generalized concept lattice,” Logic Journal of IGPL, 13, (5), pp. 543-550, 2005.
- [22] D. Maier, “The Theory of Relational Databases,” Computer Science Press, Rockville, 1983.
- [23] O. Ore, “Galois connections,” Trans. Amer. Math. Soc., 55, pp. 493-513, 1944.
- [24] S. Pollandt, “Fuzzy Begriffe,” Springer, Berlin, 1997.
- [25] G. Snelting and F. Tip, “Understanding class hierarchies using concept analysis,” ACM Trans. Program. Lang. Syst., 22, (3), pp. 540-582, May 2000.
- [26] G. Takeuti and S. Titani, “Globalization of intuitionistic set theory,” Annals of Pure and Applied Logic, 33, pp. 195-211, 1987.
- [27] L. A. Zadeh, “The concept of a linguistic variableand its application to approximate reasoning I, II, III,” Inf. Sci., 8, (3), pp. 199-251, 1975; pp. 301-357; 9, pp. 43-80, 1975.

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