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Published in: International Journal of Machine Learning and Cybernetics 4/2014

01-08-2014 | Original Article

Decision implications: a logical point of view

Authors: Zhai Yanhui, Li Deyu, Qu Kaishe

Published in: International Journal of Machine Learning and Cybernetics | Issue 4/2014

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Abstract

This paper serves to present the semantical and syntactical aspects of decision implications. In the semantical aspect, we will introduce the notions of “closure” and “unite closure”, representing the closure of condition attributes with respect to decision attributes and the closure with respect to the whole attribute set respectively. In the syntactical aspect, we form two deduction rules, namely Augmentation and Combination, and prove that they are complete with respect to the semantical aspect. Moreover, we describe an approach to obtain a decision context from a given set of decision implications, and show that the decision context obtained can produce the same set of decision implications.

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Literature
1.
go back to reference Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. Formal Concept Anal 83:445–470MathSciNet Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. Formal Concept Anal 83:445–470MathSciNet
2.
go back to reference Ganter B, Wille R (1999) Formal concept analysis: mathematical foundations. Springer, Berlin Ganter B, Wille R (1999) Formal concept analysis: mathematical foundations. Springer, Berlin
3.
go back to reference Qu KS, Zhai YH, Liang JY, Chen M (2007) Study of decision implications based on formal concept analysis. Int J General Syst 36(2):147–156CrossRefMATHMathSciNet Qu KS, Zhai YH, Liang JY, Chen M (2007) Study of decision implications based on formal concept analysis. Int J General Syst 36(2):147–156CrossRefMATHMathSciNet
4.
go back to reference Qu KS, Zhai YH (2008) Generating complete set of implications for formal contexts. Knowl Based Syst 21:429–433CrossRef Qu KS, Zhai YH (2008) Generating complete set of implications for formal contexts. Knowl Based Syst 21:429–433CrossRef
6.
go back to reference Song X-X, Wang X, Zhang W-X (2013) Independence of axiom sets characterizing formal concepts. Int J Mach Learn Cybern 4(5):459–468CrossRef Song X-X, Wang X, Zhang W-X (2013) Independence of axiom sets characterizing formal concepts. Int J Mach Learn Cybern 4(5):459–468CrossRef
9.
go back to reference Roth C, Obiedkov SA, Kourie DG (2006) Towards concise representation for taxonomies of epistemic communities. In: Yahia SB, Nguifo EM, Běelohlávek R (eds) Fourth international conference on concept lattices and their applications, CLA 2006. Lecture notes in computer science, vol 4923. Springer, Tunis, pp 240–255 Roth C, Obiedkov SA, Kourie DG (2006) Towards concise representation for taxonomies of epistemic communities. In: Yahia SB, Nguifo EM, Běelohlávek R (eds) Fourth international conference on concept lattices and their applications, CLA 2006. Lecture notes in computer science, vol 4923. Springer, Tunis, pp 240–255
10.
go back to reference Jay N, Kohler F, Napoli A (2008) Analysis of social communities with iceberg and stability-based concept lattices. In: Medina R, Obiedkov SA (eds) 6th International conference on formal concept analysis, ICFCA 2008. Lecture notes in computer science, vol 4933. Springer, Berlin, pp 258–272 Jay N, Kohler F, Napoli A (2008) Analysis of social communities with iceberg and stability-based concept lattices. In: Medina R, Obiedkov SA (eds) 6th International conference on formal concept analysis, ICFCA 2008. Lecture notes in computer science, vol 4933. Springer, Berlin, pp 258–272
11.
go back to reference Tonella P (2003) Using a concept lattice of decomposition slices for program understanding and impact analysis. IEEE Trans Softw Eng 29(6):495–509CrossRef Tonella P (2003) Using a concept lattice of decomposition slices for program understanding and impact analysis. IEEE Trans Softw Eng 29(6):495–509CrossRef
12.
go back to reference Dekel U (2003) Revealing java class structure with concept lattices, Master’s thesis, Master’s thesis, Technion -Israel Institute of Technology Dekel U (2003) Revealing java class structure with concept lattices, Master’s thesis, Master’s thesis, Technion -Israel Institute of Technology
13.
go back to reference Carpineto C, Romano G (2004) Concept data analysis: theory and applications. Wiley, New York Carpineto C, Romano G (2004) Concept data analysis: theory and applications. Wiley, New York
14.
go back to reference Stumme G (1996) Attribute exploration with background implications and exceptions. In: Bock H-H, Polasek W (eds) Data Analysis and Information Systems. Statistical and Conceptual approaches. Proc. GfKl’95. Studies in Classification, Data Analysis, and Knowledge Organization, vol 7. Springer, Heidelberg, pp 457–469 Stumme G (1996) Attribute exploration with background implications and exceptions. In: Bock H-H, Polasek W (eds) Data Analysis and Information Systems. Statistical and Conceptual approaches. Proc. GfKl’95. Studies in Classification, Data Analysis, and Knowledge Organization, vol 7. Springer, Heidelberg, pp 457–469
15.
go back to reference Maier D (1983) The theory of relational data bases. Computer Science Press, Rockville Maier D (1983) The theory of relational data bases. Computer Science Press, Rockville
16.
go back to reference Agrawal R, Mannila H, Srikant R, Toivonen H, Verkamo AI (1996) Advances in knowledge discovery and data mining, chap. Fast discovery of association rules. American Association for Artificial Intelligence, pp 307–328 Agrawal R, Mannila H, Srikant R, Toivonen H, Verkamo AI (1996) Advances in knowledge discovery and data mining, chap. Fast discovery of association rules. American Association for Artificial Intelligence, pp 307–328
17.
go back to reference Duquenne V, Guigues J-L (1986) Famille minimale d’implications informatives résultant d’un tableau de donn’ees binaires. Mathématiques et Sciences Humaines 24(95):5–18 Duquenne V, Guigues J-L (1986) Famille minimale d’implications informatives résultant d’un tableau de donn’ees binaires. Mathématiques et Sciences Humaines 24(95):5–18
18.
go back to reference Armstrong WW (1974) Dependency structures of data base relationships. In: IFIP Congress, pp 580–583 Armstrong WW (1974) Dependency structures of data base relationships. In: IFIP Congress, pp 580–583
19.
go back to reference Zhang W, Wei L, Qi J (2005) Attribute reduction theory and approach to concept lattice. Sci China Series F Inf Sci 48:713–726. ISSN 1009–2757 Zhang W, Wei L, Qi J (2005) Attribute reduction theory and approach to concept lattice. Sci China Series F Inf Sci 48:713–726. ISSN 1009–2757
20.
21.
go back to reference Li J, Mei C, Lv Y (2012) Knowledge reduction in formal decision contexts based on an order-preserving mapping. Int J General Syst 41(2):143–161CrossRefMATHMathSciNet Li J, Mei C, Lv Y (2012) Knowledge reduction in formal decision contexts based on an order-preserving mapping. Int J General Syst 41(2):143–161CrossRefMATHMathSciNet
23.
go back to reference Pollandt S (1997) Fuzzy Begriffe: Formale Begriffsanalyse von unscharfen Daten. Springer, Berlin Pollandt S (1997) Fuzzy Begriffe: Formale Begriffsanalyse von unscharfen Daten. Springer, Berlin
24.
go back to reference Běelohlávek R, Outrata J, Vychodil V (2006) Thresholds and shifted attributes in formal concept analysis of data with fuzzy attributes. In: 14th International conference on conceptual structures, pp 117–130 Běelohlávek R, Outrata J, Vychodil V (2006) Thresholds and shifted attributes in formal concept analysis of data with fuzzy attributes. In: 14th International conference on conceptual structures, pp 117–130
25.
go back to reference Zaki MJ, Ogihara M (1998) Theoretical foundations of association rules. In: In 3rd ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery Zaki MJ, Ogihara M (1998) Theoretical foundations of association rules. In: In 3rd ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery
26.
go back to reference Hamilton AG (1978) Logic For Mathematicians. Cambridge University Press, London Hamilton AG (1978) Logic For Mathematicians. Cambridge University Press, London
27.
go back to reference Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht
28.
Metadata
Title
Decision implications: a logical point of view
Authors
Zhai Yanhui
Li Deyu
Qu Kaishe
Publication date
01-08-2014
Publisher
Springer Berlin Heidelberg
Published in
International Journal of Machine Learning and Cybernetics / Issue 4/2014
Print ISSN: 1868-8071
Electronic ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-013-0204-2

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