The formal concept analysis gives a mathematical definition of a formal concept. However, in many real-life applications, the problem under investigation cannot be described by formal concepts. Such concepts are called the non-definable concepts (Saquer and Deogun, 2000a). The process of finding formal concepts that best describe non-definable concepts is called the concept approximation. In this paper, we present two different approaches to the concept approximation. The first approach is based on rough set theory while the other is based on a similarity measure. We present algorithms for the two approaches.
@article{bwmeta1.element.bwnjournal-article-amcv11i3p655bwm,
author = {Saquer, Jamil and Deogun, Jitender},
title = {Concept approximations based on rough sets and similarity measures},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {11},
year = {2001},
pages = {655-674},
zbl = {0990.68146},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv11i3p655bwm}
}
Saquer, Jamil; Deogun, Jitender. Concept approximations based on rough sets and similarity measures. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) pp. 655-674. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv11i3p655bwm/
[000] Carpineto C. and Romano G. (1996): A lattice conceptual clustering system and its application to browsing retrieval. - Mach. Learn., Vol.24, No.2, pp.95-122.
[001] Ganter B. (1984): Two basic algorithms in concept analysis. - FB4-Preprint No. 831, TH Darmstadt. | Zbl 1274.68484
[002] Ganter B. and Wille R. (1999): Formal Concept Analysis: Mathematical Foundations. - Berlin: Springer. | Zbl 0909.06001
[003] Godin R. and Missaoui R. (1994): An incremental concept formation for learning from databases. - Theoret. Comp. Sci., Vol.133, No.2, pp.387-419. | Zbl 0938.68806
[004] Ho T.B. (1995): An approach to concept formation based on Formal Concept Analysis. - IEICE Trans. Inform. Syst., Vol.78, No.5, pp.553-559.
[005] Kangassalo H. (1992): On the concept of concept for conceptualmodeling and concept deduction, In: Information Modeling and Knowledge Bases III (S. Ohsuga, H. Kangassalo and H. Jaakkola, Eds.). - Amsterdam: IOS Press, pp.17-58.
[006] Kent R. (1994): Rough concept analysis. - Proc. Int. Workshop Rough Sets and Knowledge Discovery, Banff, Canada, pp.245-253.
[007] Kent R. (1996): Rough concept analysis: A synthesis of roughsets and formal concept analysis. - Fund. Inform., Vol.27, No.2, pp.169-181. | Zbl 0861.68098
[008] Pawlak Z. (1982): Rough sets. - Int. J. Inf. Comp. Sci., Vol.11, No.5, pp.341-356. | Zbl 0501.68053
[009] Saquer J. and Deogun J. (1999): Formal rough concept analysis, In: New Directions in Rough Sets, Data Mining, and Granular-Soft Computing (N. Zhong, A. Skowron and S. Ohsuga, Eds.). - Yamaguchi, Japan: Springer, pp.91-99. | Zbl 0954.68137
[010] Saquer J. and Deogun J. (2000a): Concept approximations for formal concept analysis. - Proc. 8-th Int. Conf. Conceptual Structures (ICCS'2000), Vol.II, Working with Conceptual Structures, Darmstadt, Germany, pp.73-83. | Zbl 0954.68137
[011] Saquer J. and Deogun J. (2000b): Using closed itemsets for discovering representative association rules, In:Proc. 12-th Int. Symp. Methodologies for Intelligent Systems (ISMIS'2000) (Z. Ras and S. Ohsuga, Eds.). - Charlotte, NC: Springer, pp.495-504. | Zbl 0983.68517
[012] Wille R. (1992): Concept lattices and conceptual knowledge systems. - Comp. Math. Appl., Vol.23., No.5, pp.493-515. | Zbl 0766.68129
[013] Wille R. (1982): Restructuring lattice theory: An approach based on hierarchies on concepts, In: Ordered Sets (I. Rival, Ed.). - Dordrecht: Reidel, pp.445-470.
[014] Wille R. (1989): Knowledge acquisition by methods of formal concept analysis, In: Data Analysis, Learning Symbolic and Numeric Knowledge (E. Diday, Ed.). - New York: Nova Science,pp.365-380.
[015] Zadeh L. (1965): Fuzzy sets. - Inform. Contr., Vol.8, pp.338-353. | Zbl 0139.24606