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An information fusion technology for triadic decision contexts

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Abstract

In this paper, the notion of a projected context is proposed to explore a novel algorithm of computing triadic concepts of a triadic context, and a triadic decision context is defined by combining triadic contexts. Then a rule acquisition method is presented for triadic decision contexts. It can be considered as an information fusion technology for decision-making analysis of multi-source data if the data under each condition is viewed as a single-source data. Moreover, a knowledge reduction framework is established to simplify knowledge discovery. Finally, discernibility matrix and Boolean function are constructed to compute all reducts, which is beneficial to the acquisition of compact rules from a triadic decision context.

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References

  1. Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival I (ed) Ordered sets. Reidel, Dordrecht, pp 445–470

    Chapter  Google Scholar 

  2. Zhang WX, Wei L, Qi JJ (2005) Attribute reduction theory and approach to concept lattice. Science in China F 48(6):713–726

    Article  MATH  MathSciNet  Google Scholar 

  3. Ganter B, Wille R (1999) Formal concept analysis. Mathematical foundations. Springer, Berlin

    Book  MATH  Google Scholar 

  4. Wang LD, Liu XD (2008) Concept analysis via rough set and AFS algebra. Inf Sci 178:4125–4137

    Article  MATH  Google Scholar 

  5. Aswani Kumar Ch, Srinivas S (2010) Concept lattice reduction using fuzzy K-means clustering. Expert Syst Appl 37(3):2696–2704

    Article  Google Scholar 

  6. Ma JM, Zhang WX (2013) Axiomatic characterizations of dual concept lattices. Int J Approx Reason 54(5):690–697

    Article  Google Scholar 

  7. Zou LG, Zhang ZP, Long J (2015) A fast incremental algorithm for constructing concept lattices. Expert Syst Appl 42(9):4474–4481

    Article  Google Scholar 

  8. Li TJ, Wu WZ (2011) Attribute reduction in formal contexts: a covering rough set approach. Fundam Inform 111(1):15–32

    MATH  Google Scholar 

  9. Lehmann F, Wille R (1995) A triadic approach to formal concept analysis. Lecture Notes in Computer Science 954:32–43

  10. Wille R (1995) The basic theorem of triadic concept analysis. Order 12(2):149–158

    Article  MATH  MathSciNet  Google Scholar 

  11. Dau F, Wille R (2000) On the modal understanding of triadic contexts. In: Decker R, Gaul W (eds) Studies in classification, data analysis, and knowledge organization. Springer, Berlin, pp 83–94

    Google Scholar 

  12. Konecny J, Osicka P (2010) General approach to triadic concept analysis. In: Proceedings of CLA, pp 116–126

  13. Belohlavek R, Glodeanu C, Vychodil V (2013) Optimal factorization of three-way binary data using triadic concepts. Order 30(2):437–454

    Article  MATH  MathSciNet  Google Scholar 

  14. Wei L, Wan Q, Qian T, Qi JJ (2014) An overview of triadic concept analysis. J Northwest Univ 44(5):689–699 (in Chinese)

    MathSciNet  Google Scholar 

  15. Tang YQ, Fan M, Li JH (2014) Cognitive system model and approach to transformation of information granules under triadic formal concept analysis. J Shandong Univ 49(8):102–106 (in Chinese)

    MATH  MathSciNet  Google Scholar 

  16. Zhang WX, Qiu GF (2005) Uncertain decision making based on rough sets. Tsinghua University Press, Beijing

    Google Scholar 

  17. Shao MW (2007) Knowledge acquisition in decision formal contexts. In: Proceedings of the sixth international conference on machine learning and cybernetics, Hong Kong, pp 4050–4054

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

    Article  MATH  MathSciNet  Google Scholar 

  19. Wei L, Qi JJ, Zhang WX (2008) Attribute reduction theory of concept lattice based on decision formal contexts. Sci China F 51(7):910–923

    Article  MATH  MathSciNet  Google Scholar 

  20. Wang H, Zhang W (2008) Approaches to knowledge reduction in generalized consistent decision formal context. Math Comput Model 48(11–12):1677–1684

    Article  MATH  Google Scholar 

  21. Wu WZ, Leung Y, Mi JS (2009) Granular computing and knowledge reduction in formal contexts. IEEE Trans Knowl Data Eng 21(10):1461–1474

    Article  Google Scholar 

  22. Shao MW, Leung Y, Wu WZ (2013) Rule acquisition and complexity reduction in formal decision contexts. Int J Approx Reason 55(1):259–274

    Article  MathSciNet  Google Scholar 

  23. Li J, Mei C, Lv Y (2012a) Knowledge reduction in formal decision contexts based on an order-preserving mapping. Int J Gen Syst 41(2):143–161

    Article  MATH  MathSciNet  Google Scholar 

  24. Li J, Mei C, Lv Y (2011a) A heuristic knowledge-reduction method for decision formal contexts. Comput Math Appl 61(4):1096–1106

    Article  MATH  MathSciNet  Google Scholar 

  25. Li J, Mei C, Lv Y (2011b) Knowledge reduction in decision formal contexts. Knowl Based Syst 24:709–715

    Article  Google Scholar 

  26. Li J, Mei C, Wang J, Zhang X (2014) Rule-preserved object compression in formal decision contexts using concept lattices. Knowl Based Syst 71:435–445

    Article  Google Scholar 

  27. Hong WX, Yu JP, Cai F, Song JL (2012) A new method of attribute reduction for decision formal context. ICIC Express Lett B Appl 3(5):1061–1068

    Google Scholar 

  28. Li J, Mei C, Lv Y (2013) Incomplete decision contexts: approximate concept construction, rule acquisition and knowledge reduction. Int J Approx Reason 54(1):149–165

    Article  MATH  MathSciNet  Google Scholar 

  29. Pei D, Li MZ, Mi JS (2011) Attribute reduction in fuzzy decision formal contexts. In: International conference on machine learning and cybernetics. IEEE Press, New York, pp 204–208

  30. Kang XP, Li DY, Wang SG, Qu KS (2012) Formal concept analysis based on fuzzy granularity base for different granulations. Fuzzy Sets Syst 203:33–48

    Article  MATH  MathSciNet  Google Scholar 

  31. Li J, Mei C, Lv Y (2012) Knowledge reduction in real decision formal contexts. Inf Sci 189:191–207

    Article  MATH  MathSciNet  Google Scholar 

  32. Li J, Mei C, Lv Y, Zhang X (2012) A heuristic knowledge reduction algorithm for real decision formal contexts. In: Yao JT et al (eds) Proceedings of RSCTC, Lecture Notes in Artificial Intelligence, vol 7413. Springer, Berlin, pp 303–312

  33. Yang HZ, Leung Y, Shao MW (2011) Rule acquisition and attribute reduction in real decision formal contexts. Soft Comput 15(6):1115–1128

    Article  MATH  Google Scholar 

  34. Jschke R, Hotho A, Schmitz C, et al (2006) TRIAS—an algorithm for mining iceberg tri-lattices. In: Proceeding of the sixth international conference on data mining. Hong Kong, pp 907–911

  35. Missaoui R, Kwuida L (2011) Mining triadic association rules from ternary relations. In: Proceeding of ICFCA, Lecture Notes in Computer Science, vol 6628. Springer, Berlin, pp 204–218

  36. Ignatov DI, Gnatyshak DV, Kuznetsov SO et al (2015) Triadic formal concept analysis and triclustering: searching for optimal patterns. Mach Learn. doi:10.1007/s10994-015-5487-y

  37. Aswani Kumar C (2013) Designing role-based access control using formal concept analysis. Secur Commun Netw 6(3):373–383

    Article  Google Scholar 

  38. Li J, Mei C, Xu W, Qian Y (2015) Concept learning via granular computing: a cognitive viewpoint. Inf Sci 298:447–467

    Article  MathSciNet  Google Scholar 

  39. Wang XZ, Xing HJ, Li Y et al (2014) A study on relationship between generalization abilities and fuzziness of base classifiers in ensemble learning. IEEE Trans Fuzzy Syst. doi:10.1109/TFUZZ.2014.2371479

  40. Wang XZ, Dong LC, Yan JH (2012) Maximum ambiguity based sample selection in fuzzy decision tree induction. IEEE Trans Knowl Data Eng 24(8):1491–1505

    Article  Google Scholar 

  41. Wang XZ, Dong CR (2009) Improving generalization of fuzzy if–then rules by maximizing fuzzy entropy. IEEE Trans Fuzzy Syst 17(3):556–567

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to thank anonymous reviewers for their valuable comments and suggestions which lead to a significant improvement on the manuscript. This work was supported by the National Natural Science Foundation of China (Nos. 61305057, 61562050 and 61573173) and the Natural Science Research Foundation of Kunming University of Science and Technology (No. 14118760).

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Correspondence to Jinhai Li.

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Tang, Y., Fan, M. & Li, J. An information fusion technology for triadic decision contexts. Int. J. Mach. Learn. & Cyber. 7, 13–24 (2016). https://doi.org/10.1007/s13042-015-0411-0

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  • DOI: https://doi.org/10.1007/s13042-015-0411-0

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