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Relating attribute reduction in formal, object-oriented and property-oriented concept lattices. (English) Zbl 1268.06007

Summary: Attribute reduction is an important step in reducing computational complexity in order to extract information from relational systems.
Three of these systems are the formal, object-oriented and property oriented concept lattices. Attribute reduction in the last two concept lattices has recently been studied. The relation with the first concept lattice is very important since two important, independent tools to extract information from databases – the formal concept analysis and rough set theory – will be related. This paper studies attribute reduction in these three frameworks. The main results are that the classification of each attribute into absolutely necessary, relatively necessary and absolutely unnecessary attributes is independent of the framework considered and that an attribute reduct in one of these relational systems is also an attribute reduct in the others.

MSC:

06B23 Complete lattices, completions
06A15 Galois correspondences, closure operators (in relation to ordered sets)
68T30 Knowledge representation
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[1] Pawlak, Z., Rough sets, International journal of computer and information science, 11, 341-356, (1982) · Zbl 0501.68053
[2] Düntsch, I.; Gediga, G., Approximation operators in qualitative data analysis, (), 214-230 · Zbl 1203.68193
[3] G. Gediga, I. Düntsch, Modal-style operators in qualitative data analysis, in: Proc. IEEE Int. Conf. on Data Mining, 2002, pp. 155-162.
[4] Chen, Y.; Yao, Y., A multiview approach for intelligent data analysis based on data operators, Information sciences, 178, 1, 1-20, (2008) · Zbl 1126.68593
[5] Yao, Y.Y., A comparative study of formal concept analysis and rough set theory in data analysis, Lecture notes in artificial intelligence, 3066, 59-68, (2004) · Zbl 1103.68123
[6] Wang, X.; Zhang, W., Relations of attribute reduction between object and property oriented concept lattices, Knowledge-based systems, 21, 398-403, (2008)
[7] Min Liu, M.S.; Zhang, W.; Wu, C., Reduction method for concept lattices based on rough set theory and its application, Computers and mathematics with applications, 53, 1390-1410, (2007) · Zbl 1121.68113
[8] Qu, K.-S.; Zhai, Y.-H., Generating complete set of implications for formal contexts, Knowledge-based systems, 21, 429-433, (2008)
[9] Arévalo, G.; Ducasse, S.; Gordillo, S.; Nierstraszn, O., Generating a catalog of unanticipated schemas in class hierarchies using formal concept analysis, Information and software technology, 52, 11, 1167-1187, (2010)
[10] Formica, A., Concept similarity in fuzzy formal concept analysis for semantic web, International journal of uncertainty, fuzziness and knowledge-based systems, 18, 2, 153-167, (2010)
[11] Galitsky, B.; Rosa, J.D.L., Concept-based learning of human behavior for customer relationship management, Information sciences, 181, 10, 2016-2035, (2011)
[12] ()
[13] Kumar, C.; Srinivas, S., Mining associations in health care data using formal concept analysis and singular value decomposition, Journal of biological systems, 18, 4, 787-807, (2010)
[14] Poelmans, J.; Elzinga, P.; Viaene, S.; Deden, G., Formal concept analysis in knowledge discovery: a survey, Lecture notes in computer science, 6208, 139-153, (2010)
[15] Phan-Luong, V., A framework for integrating information sources under lattice structure, Information fusion, 9, 278-292, (2008)
[16] Beydoun, G., Formal concept analysis for an e-learning semantic web, Expert systems with applications, 36, 8, 10952-10961, (2009)
[17] Formica, A., Semantic web search based on rough sets and fuzzy formal concept analysis, Knowledge-based systems, 26, 40-47, (2012)
[18] Ganter, B.; Wille, R., Formal concept analysis: mathematical foundation, (1999), Springer Verlag
[19] J. Medina, M.O. Aciego, Towards attribute reduction in multi-adjoint concept lattices, in: The 7th International Conference on Concept Lattices and Their Applications, 2010, pp. 92-103.
[20] Davey, B.; Priestley, H., Introduction to lattices and order, (2002), Cambridge University Press · Zbl 1002.06001
[21] Zhang, W.; Wei, L.; Qi, J., Attribute reduction in concept lattice based on discernibility matrix, Lecture notes in computer science, 3642, 157-165, (2005) · Zbl 1155.68525
[22] Yao, Y.Y.; Chen, Y., Rough set approximations in formal concept analysis, (), 285-305 · Zbl 1136.68527
[23] Chen, X.; Li, Q., Construction of rough approximations in fuzzy setting, Fuzzy sets and systems, 158, 23, 2641-2653, (2007) · Zbl 1127.68105
[24] Liu, G.L., Generalized rough set over fuzzy lattices, Information sciences, 178, 6, 1651-1662, (2008) · Zbl 1136.03328
[25] Djouadi, Y.; Prade, H., Possibility-theoretic extension of derivation operators in formal concept analysis over fuzzy lattices, Fuzzy optimization and decision making, 4, 287-309, (2011) · Zbl 1254.06005
[26] Dubois, D.; de Saint-Cyr, F.D.; Prade, H., A possibility-theoretic view of formal concept analysis, Fundamenta informaticae, 75, 1-4, 195-213, (2007) · Zbl 1108.68114
[27] Radzikowska, A.M.; Kerre, E.E., A comparative study of fuzzy rough sets, Fuzzy sets and systems, 126, 2, 137-155, (2002) · Zbl 1004.03043
[28] Lai, H.; Zhang, D., Concept lattices of fuzzy contexts: formal concept analysis vs. rough set theory, International journal of approximate reasoning, 50, 5, 695-707, (2009) · Zbl 1191.68658
[29] Georgescu, G.; Popescu, A., Non-dual fuzzy connections, Archive for mathematical logic, 43, 8, 1009-1039, (2004) · Zbl 1060.03042
[30] Wille, R., Restructuring lattice theory: an approach based on hierarchies of concepts, (), 445-470
[31] Y.Y. Yao, Concept lattices in rough set theory, in: Proceedings of Annual Meeting of the North American Fuzzy Information Processing Society, NAFIPS’04, 2004, pp. 796-801.
[32] Medina, J., Multi-adjoint property-oriented and object-oriented concept lattices, Information sciences, 190, 95-106, (2012) · Zbl 1248.68479
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