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Erschienen in: Soft Computing 6/2011

01.06.2011 | Focus

Rule acquisition and attribute reduction in real decision formal contexts

verfasst von: Hong-Zhi Yang, Leung Yee, Ming-Wen Shao

Erschienen in: Soft Computing | Ausgabe 6/2011

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Abstract

Formal Concept Analysis of real set formal contexts is a generalization of classical formal contexts. By dividing the attributes into condition attributes and decision attributes, the notion of real decision formal contexts is introduced. Based on an implication mapping, problems of rule acquisition and attribute reduction of real decision formal contexts are examined. The extraction of “if–then” rules from the real decision formal contexts, and the approach to attribute reduction of the real decision formal contexts are discussed. By the proposed approach, attributes which are non-essential to the maximal s rules or l rules (to be defined later in the text) can be removed. Furthermore, discernibility matrices and discernibility functions for computing the attribute reducts of the real decision formal contexts are constructed to determine all attribute reducts of the real set formal contexts without affecting the results of the acquired maximal s rules or l rules.

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Literatur
Zurück zum Zitat Beynon M (2001) Reducts within the variable precision rough sets model: a further investigation. Eur J Oper Res 134:592–605MATHCrossRef Beynon M (2001) Reducts within the variable precision rough sets model: a further investigation. Eur J Oper Res 134:592–605MATHCrossRef
Zurück zum Zitat Burusco A, Fuentes-González R (2000) Concept lattices defined from implication operators. Fuzzy Sets Syst 114(3):431–436MATHCrossRef Burusco A, Fuentes-González R (2000) Concept lattices defined from implication operators. Fuzzy Sets Syst 114(3):431–436MATHCrossRef
Zurück zum Zitat Carpineto C, Romano G (1996) A lattice conceptual clustering system and its application to browsing retrieval. Mach Learn 10:95–122 Carpineto C, Romano G (1996) A lattice conceptual clustering system and its application to browsing retrieval. Mach Learn 10:95–122
Zurück zum Zitat Chen D, Wang C, Hu Q (2007) A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets. Info Sci 177:3500–3518MATHCrossRef Chen D, Wang C, Hu Q (2007) A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets. Info Sci 177:3500–3518MATHCrossRef
Zurück zum Zitat Elloumi S, Jaam J, Hasnah A, Jaoua A, Nafkha I (2004) A multi-level conceptual data reduction approach based on the Lukasiewicz implication. Info Sci 163:253–262MathSciNetMATHCrossRef Elloumi S, Jaam J, Hasnah A, Jaoua A, Nafkha I (2004) A multi-level conceptual data reduction approach based on the Lukasiewicz implication. Info Sci 163:253–262MathSciNetMATHCrossRef
Zurück zum Zitat Faid M, Missaoi R, Godin R (1997) Mining complex structures using context concatenation in formal concept analysis. International KRUSE Symposium, Vancouver, BC, pp 11–13 Faid M, Missaoi R, Godin R (1997) Mining complex structures using context concatenation in formal concept analysis. International KRUSE Symposium, Vancouver, BC, pp 11–13
Zurück zum Zitat Gediga B, Wille R (1999) Formal concept analysis, mathematic foundations. Springer, Berlin Gediga B, Wille R (1999) Formal concept analysis, mathematic foundations. Springer, Berlin
Zurück zum Zitat Godin R, Missaoi R (1994) An incremental concept formation approach for learning from databases. Theor Comput Sci 133:387–419MATHCrossRef Godin R, Missaoi R (1994) An incremental concept formation approach for learning from databases. Theor Comput Sci 133:387–419MATHCrossRef
Zurück zum Zitat Harms SK, Deogum JS (2004) Sequential association rule mining with time lags. J Intell Info Syst 22(1):7–22CrossRef Harms SK, Deogum JS (2004) Sequential association rule mining with time lags. J Intell Info Syst 22(1):7–22CrossRef
Zurück zum Zitat Hu QH, Xie ZX, Yu DR (2007) Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation. Pattern Recogn 40(12):3509–3521MATHCrossRef Hu QH, Xie ZX, Yu DR (2007) Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation. Pattern Recogn 40(12):3509–3521MATHCrossRef
Zurück zum Zitat Jaoua A, Elloumi S (2002) Galois connection, formal concepts and Galois lattice in real relations: application in a real classifier. J Syst Softw 60:149–163CrossRef Jaoua A, Elloumi S (2002) Galois connection, formal concepts and Galois lattice in real relations: application in a real classifier. J Syst Softw 60:149–163CrossRef
Zurück zum Zitat Ke LJ, Feng ZR, Ren ZG (2008) An efficient ant colony optimization approach to attribute reduction in rough set theory. Pattern Recogn Lett 29(9):1351–1357CrossRef Ke LJ, Feng ZR, Ren ZG (2008) An efficient ant colony optimization approach to attribute reduction in rough set theory. Pattern Recogn Lett 29(9):1351–1357CrossRef
Zurück zum Zitat Krajči S (2003) Cluster based efficient generation of fuzzy concepts. Neural Netw World 5:521–530 Krajči S (2003) Cluster based efficient generation of fuzzy concepts. Neural Netw World 5:521–530
Zurück zum Zitat Liu M, Shao MW, Zhang WX, Wu C (2007) Reduction method for concept lattices based on rough set theory and its application. Comput Math Appl 53(9):1390–1410MathSciNetMATHCrossRef Liu M, Shao MW, Zhang WX, Wu C (2007) Reduction method for concept lattices based on rough set theory and its application. Comput Math Appl 53(9):1390–1410MathSciNetMATHCrossRef
Zurück zum Zitat Mi JS, Wu WZ, Zhang WX (2004) Approaches to knowledge reductions based on variable precision rough sets model. Info Sci 159(3–4):255–272MathSciNetMATHCrossRef Mi JS, Wu WZ, Zhang WX (2004) Approaches to knowledge reductions based on variable precision rough sets model. Info Sci 159(3–4):255–272MathSciNetMATHCrossRef
Zurück zum Zitat Popescu A (2001) A general approach to fuzzy concept. Math Logic Q 50(3):1–17 Popescu A (2001) A general approach to fuzzy concept. Math Logic Q 50(3):1–17
Zurück zum Zitat Skowron A (1993) A synthesis of decision rules: applications of discernibility matrix. In: Proceedings of the international conference on intelligent information systems, Augustow, Poland, pp 30–46 Skowron A (1993) A synthesis of decision rules: applications of discernibility matrix. In: Proceedings of the international conference on intelligent information systems, Augustow, Poland, pp 30–46
Zurück zum Zitat Skowron A, Rauszer C (1992) The discernibility matrices and functions in information systems. In: Slowinski R (ed) Intelligent decision support: handbook of applications and advances of rough sets theory. Kluwer, Dordrecht, pp 331–362 Skowron A, Rauszer C (1992) The discernibility matrices and functions in information systems. In: Slowinski R (ed) Intelligent decision support: handbook of applications and advances of rough sets theory. Kluwer, Dordrecht, pp 331–362
Zurück zum Zitat Starzyk JA, Nelson DE, Sturtz K (2000) A mathematical foundation for improved reduct generation in information systems. Knowl Info Syst 2:131–146MATHCrossRef Starzyk JA, Nelson DE, Sturtz K (2000) A mathematical foundation for improved reduct generation in information systems. Knowl Info Syst 2:131–146MATHCrossRef
Zurück zum Zitat Wang GY (2003) Rough reduction in algebra view and information view. Int J Intell Syst 18:679–688MATHCrossRef Wang GY (2003) Rough reduction in algebra view and information view. Int J Intell Syst 18:679–688MATHCrossRef
Zurück zum Zitat Wang X, Zhang WX (2008) Relations of attribute reduction between object and property oriented concept lattices. Knowl Based Syst 21(5):398–403CrossRef Wang X, Zhang WX (2008) Relations of attribute reduction between object and property oriented concept lattices. Knowl Based Syst 21(5):398–403CrossRef
Zurück zum Zitat Wei L, Qi JJ, Zhang WX (2008) Attribute reduction theory of concept lattice based on decision formal contexts. Sci China Ser F Info Sci 51(7):910–923MathSciNetCrossRef Wei L, Qi JJ, Zhang WX (2008) Attribute reduction theory of concept lattice based on decision formal contexts. Sci China Ser F Info Sci 51(7):910–923MathSciNetCrossRef
Zurück zum Zitat Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival I (ed) Ordered sets. Reidel, Dordrecht, pp 445–470 Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival I (ed) Ordered sets. Reidel, Dordrecht, pp 445–470
Zurück zum Zitat Wu WZ (2008) Attribute reduction based on evidence theory in incomplete decision systems. Info Sci 178(5):1355–1371MATHCrossRef Wu WZ (2008) Attribute reduction based on evidence theory in incomplete decision systems. Info Sci 178(5):1355–1371MATHCrossRef
Zurück zum Zitat Wu WZ, Zhang M, Li HZ, Mi JS (2005) Knowledge reductions in random information systems via Dempster–Shafer theory of evidence. Info Sci 174(3–4):143–165MathSciNetMATHCrossRef Wu WZ, Zhang M, Li HZ, Mi JS (2005) Knowledge reductions in random information systems via Dempster–Shafer theory of evidence. Info Sci 174(3–4):143–165MathSciNetMATHCrossRef
Zurück zum Zitat Wu WZ, Yee Y, Mi JS (2009) Granular computing and knowledge reduction in formal contexts. IEEE Trans Knowl Data Eng 21(10): 1461–1474CrossRef Wu WZ, Yee Y, Mi JS (2009) Granular computing and knowledge reduction in formal contexts. IEEE Trans Knowl Data Eng 21(10): 1461–1474CrossRef
Zurück zum Zitat Yahia S, Jaoua A (2001) Discovering knowledge from fuzzy concept lattice[A]. In: Kandel A, Last M, Bunke H (ed) Data mining and computational intelligence[C], Physica-Verlag, Heidelberg, pp 167–190 Yahia S, Jaoua A (2001) Discovering knowledge from fuzzy concept lattice[A]. In: Kandel A, Last M, Bunke H (ed) Data mining and computational intelligence[C], Physica-Verlag, Heidelberg, pp 167–190
Zurück zum Zitat Yang XB, Yang JY, Wu C et al (2008) Dominance-based rough set approach and knowledge reductions in incomplete ordered information system. Info Sci 178(4):1219–1234MathSciNetMATHCrossRef Yang XB, Yang JY, Wu C et al (2008) Dominance-based rough set approach and knowledge reductions in incomplete ordered information system. Info Sci 178(4):1219–1234MathSciNetMATHCrossRef
Zurück zum Zitat Zhang WX, Wu WZ, Liang JY, Li DY (2001) Theory and method of rough sets. Science Press, Beijing Zhang WX, Wu WZ, Liang JY, Li DY (2001) Theory and method of rough sets. Science Press, Beijing
Zurück zum Zitat Zhang WX, Mi JS, Wu WZ (2003) Approaches to knowledge reductions in inconsistent systems. Int J Intell Syst 21:989–1000CrossRef Zhang WX, Mi JS, Wu WZ (2003) Approaches to knowledge reductions in inconsistent systems. Int J Intell Syst 21:989–1000CrossRef
Zurück zum Zitat Zhang WX, Wei L, Qi JJ (2005) Attribute reduction theory and approach of concept lattices. Sci China Ser E Info Sci 35(6):628–639MathSciNet Zhang WX, Wei L, Qi JJ (2005) Attribute reduction theory and approach of concept lattices. Sci China Ser E Info Sci 35(6):628–639MathSciNet
Metadaten
Titel
Rule acquisition and attribute reduction in real decision formal contexts
verfasst von
Hong-Zhi Yang
Leung Yee
Ming-Wen Shao
Publikationsdatum
01.06.2011
Verlag
Springer-Verlag
Erschienen in
Soft Computing / Ausgabe 6/2011
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-010-0578-y

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