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Decision implications: a logical point of view

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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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References

  1. Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. Formal Concept Anal 83:445–470

    MathSciNet  Google Scholar 

  2. Ganter B, Wille R (1999) Formal concept analysis: mathematical foundations. Springer, Berlin

  3. Qu KS, Zhai YH, Liang JY, Chen M (2007) Study of decision implications based on formal concept analysis. Int J General Syst 36(2):147–156

    Article  MATH  MathSciNet  Google Scholar 

  4. Qu KS, Zhai YH (2008) Generating complete set of implications for formal contexts. Knowl Based Syst 21:429–433

    Article  Google Scholar 

  5. Shao M, Yang H (2012) Two kinds of multi-level formal concepts and its application for sets approximations. Int J Mach Learn Cybern. doi:10.1007/s13042-012-0128-2

  6. Song X-X, Wang X, Zhang W-X (2013) Independence of axiom sets characterizing formal concepts. Int J Mach Learn Cybern 4(5):459–468

    Article  Google Scholar 

  7. Sarmah AK, Hazarika SM, Sinha SK (2013) Formal concept analysis: current trends and directions. Artif Intell Rev, pp 1–40. doi:10.1007/s10462-013-9404-0.

  8. Zupan B, Bohanec M, Demsar J, Bratko I (1999) Learning by discovering concept hierarchies. Artif Intell 109:211–242

    Article  MATH  MathSciNet  Google Scholar 

  9. 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. 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. Tonella P (2003) Using a concept lattice of decomposition slices for program understanding and impact analysis. IEEE Trans Softw Eng 29(6):495–509

    Article  Google Scholar 

  12. Dekel U (2003) Revealing java class structure with concept lattices, Master’s thesis, Master’s thesis, Technion -Israel Institute of Technology

  13. Carpineto C, Romano G (2004) Concept data analysis: theory and applications. Wiley, New York

  14. 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. Maier D (1983) The theory of relational data bases. Computer Science Press, Rockville

  16. 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. 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

    Google Scholar 

  18. Armstrong WW (1974) Dependency structures of data base relationships. In: IFIP Congress, pp 580–583

  19. 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

    Google Scholar 

  20. Li J, Mei C, Lv Y (2011) A heuristic knowledge-reduction method for decision formal contexts. Comput Math Appl 61:1096–1106

    Article  MATH  MathSciNet  Google Scholar 

  21. 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):143–161

    Article  MATH  MathSciNet  Google Scholar 

  22. Li J, Mei C, Kumar C, Zhang X (2013) On rule acquisition in decision formal contexts. Int J Mach Learn Cybern doi:10.1007/s13042-013-0150-z

  23. Pollandt S (1997) Fuzzy Begriffe: Formale Begriffsanalyse von unscharfen Daten. Springer, Berlin

  24. 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. 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. Hamilton AG (1978) Logic For Mathematicians. Cambridge University Press, London

  27. Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht

  28. Wei W, Liang J, Qian Y, Wang F, Dang C (2010) Comparative study of decision performance of decision tables induced by attribute reductions. Int J General Syst 39:813–838. doi:10.1080/03081079.2010.499102

    Google Scholar 

  29. Zhai YH, Qu KS (2009) On characteristics of information system homomorphisms. Theory Comput Syst 44:414–431

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the manuscript. The work is supported by National Natural Science Foundation of China (61303107, 61272095, 61175067, 41101440, 61202018), and Project Supported by National Science and Technology (2012BAH33B01).

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Authors and Affiliations

  1. School of Computer and Information Technology, Shanxi University, Taiyuan, 030006, China

    Zhai Yanhui, Li Deyu & Qu Kaishe

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  1. Zhai Yanhui
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  2. Li Deyu
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  3. Qu Kaishe
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Correspondence to Zhai Yanhui.

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Yanhui, Z., Deyu, L. & Kaishe, Q. Decision implications: a logical point of view. Int. J. Mach. Learn. & Cyber. 5, 509–516 (2014). https://doi.org/10.1007/s13042-013-0204-2

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