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On generalization reducts in incomplete multi-scale decision tables

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Abstract

In reality, data is always arranged at multiple granularity levels. Multi-scale information tables were introduced from the viewpoint of granular computing to represent such types of data sets. In the present paper, we focus on acquisition of if-then rules in incomplete multi-scale decision tables (IMSDT for short). The notion of generalization reducts is proposed to achieve the desired goal. By firstly considering the generalization reducts of an IMSDT and then calculating the generalization reducts for each object, a collection of optimal decision rules can be thus obtained. During the entire process of generalization reducts, both the number and the generalization ability of the original attribute set are taken into consideration. It is shown that a more general and simple set of decision rules can be obtained by using generalization reducts, compared with the approaches in the literature. Lastly, an explanatory example is employed to show the advantage of our approach, and an experiment is designed for performing a comparative study between different approaches.

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Data availability

The datasets generated during and analysed during the current study are available in the UCI repository, http://archive.ics.uci.edu/ml/datasets.php

References

  1. Bělohlávek R, De Baets B, Konecny J (2014) Granularity of attributes in formal concept analysis. Inform Sci 260:149–170

    Article  MathSciNet  Google Scholar 

  2. Feng QR, Miao DQ, Cheng Y (2010) Hierarchical decision rules mining. Expert Syst Appl 37:2081–2091

    Article  Google Scholar 

  3. Gu SM, Wu WZ (2013) On knowledge acquisition in multi-scale decision systems. Int J Mach Learn Cybern 4(5):477–486

    Article  Google Scholar 

  4. Huang B, Li HX, Feng GF, Zhou XZ (2019) Dominance-based rough sets in multi-scale intuitionistic fuzzy decision tables. Appl Math Comput 348:487–512

    MathSciNet  Google Scholar 

  5. Hao C, Li JH, Min F, Liu WQ, Tsang ECC (2017) Optimal scale selection in dynamic MSDTs based on sequential three-way decisions. Inf Sci 415:213–232

    Article  Google Scholar 

  6. Hong TP, Liou YL, Wang SL (2009) Fuzzy rough sets with hierarchical quantitative attributes. Expert Syst Appl 36:6790–6799

    Article  Google Scholar 

  7. Hong TP, Lin CE, Lin JH, Wang SL (2008) Learning cross-level certain and possible rules by rough sets. Expert Syst Appl 34(3):1698–1706

    Article  Google Scholar 

  8. Huang ZH, Li JJ, Dai WZ, Lin RD (2019) Generalized multi-scale decision tables with multi-scale decision attributes. Int J Approx Reason 115:194–208

    Article  MathSciNet  Google Scholar 

  9. Kryszkiewicz M (2001) Comparative study of alternative types of knowledge reduction in inconsistent systems. Int J Intell Syst 16(1):105–120

    Article  Google Scholar 

  10. Kryszkiewicz M (1998) Rough set approach to incomplete information systems. Inf Sci 112(1–4):39–49

    Article  MathSciNet  Google Scholar 

  11. Luo C, Li TR, Chen H, Fujita H, Zhang Y (2018) Incremental rough set approach for hierarchical multicriteria classification. Inf Sci 429:72–87

    Article  MathSciNet  Google Scholar 

  12. Luo C, Li TR, Huang YY, Fujita H (2019) Updating three-way decisions in incomplete multi-scale information systems. Inf Sci 476:274–289

    Article  Google Scholar 

  13. Li F, Hu BQ (2017) A new approach of optimal scale selection to multi-scale decision tables. Inf Sci 381:193–208

    Article  Google Scholar 

  14. Liang JY, Xu ZB (2002) The algorithm on knowledge reduction in incomplete information systems. Int J Uncertain Fuzziness Knowl-Based Syst 10(01):95–103

    Article  MathSciNet  Google Scholar 

  15. Leung Y, Wu WZ, Zhang WX (2006) Knowledge acquisition in incomplete information systems: a rough set approach. Eur J Oper Res 168(1):164–180

    Article  MathSciNet  Google Scholar 

  16. Leung Y, Li DY (2003) Maximal consistent block technique for rule acquisition in incomplete information systems. Inf Sci 153:85–106

    Article  MathSciNet  Google Scholar 

  17. Ming-Syan C, Han JW, Yu PS (1996) Data mining: an overview from a database perspective. IEEE Trans Knowl Data Eng 8:866–883

    Article  Google Scholar 

  18. Petry FE, Zhao L (2009) Data mining by attribute generalization with fuzzy hierarchies in fuzzy databases. Fuzzy Sets Syst 160(15):2206–2223

    Article  MathSciNet  Google Scholar 

  19. Qian YH, Liang JY, Pedrycz W, Dang CY (2010) Positive approximation: an accelerator for attribute reduction in rough set theory. Artif Intell 174(9–10):597–618

    Article  MathSciNet  Google Scholar 

  20. Qian YH, Liang JY, Dang CY (2009) Incomplete multigranulation rough set. IEEE Trans Syst Man Cybern Part A Syst Hum 40(2):420–431

    Article  Google Scholar 

  21. She YH, Li JH, Yang HL (2015) A local approach to rule induction in multi-scale decision tables. Knowl-Based Syst 89:398–410

    Article  Google Scholar 

  22. She YH, Qian ZH, Xiao XL et al (2021) On generalization reducts in multi-scale decision tables. Inf Sci 555:104–124

    Article  MathSciNet  Google Scholar 

  23. She YH, Zhao ZJ, Hu MJ et al (2021) On selection of optimal cuts in complete multi-scale decision tables. Artif Intell Rev 54:6125–6148

    Article  Google Scholar 

  24. She YH, He XL, Qian T et al (2019) A theoretical study on object-oriented and property-oriented multi-scale formal concept analysis. Int J Mach Learn Cybern 10:3263–3271

    Article  Google Scholar 

  25. Tan AH, Wu WZ, Li JJ, Lin GP (2016) Evidence-theory-based numerical characterization of multigranulation rough sets in incomplete information systems. Fuzzy Sets Syst 294:18–35

    Article  MathSciNet  Google Scholar 

  26. Tuo QJ, Zhao H, Hu QH (2019) Hierarchical feature selection with subtree based graph regularization. Knowl-Based Syst 163:996–1008

    Article  Google Scholar 

  27. Wu WZ, Leung Y (2011) Theory and applications of granular labelled partitions in MSDTs. Inf Sci 181:3878–3897

    Article  Google Scholar 

  28. Wu WZ, Leung Y (2013) Optimal scale selection for multi-scale decision tables. Int J Approx Reason 54(8):1107–1129

    Article  MathSciNet  Google Scholar 

  29. Wu WZ, Qian YH, Li TJ, Gu SM (2017) On rule acquisition in incomplete multi-scale decision tables. Inf Sci 378:282–302

    Article  MathSciNet  Google Scholar 

  30. Wu WZ (2008) Attribute reduction based on evidence theory in incomplete decision systems. Inf Sci 178(5):1355–1371

    Article  MathSciNet  Google Scholar 

  31. Ye MQ, Wu XD, Hu XG, Hu DH (2014) Knowledge reduction for decision tables with attribute value taxonomies. Knowl-Based Syst 56:68–78

    Article  Google Scholar 

  32. Ye MQ, Wu XD, Hu XG, Hu DH (2013) Multi-level rough set reduction for decision rule mining. Appl Intell 39(3):642–658

    Article  Google Scholar 

  33. Yang XB, Yang JY, Wu C, Yu DJ (2008) Dominance-based rough set approach and knowledge reductions in incomplete ordered information system. Inf Sci 178(4):1219–1234

    Article  MathSciNet  Google Scholar 

  34. Zhao H, Wang P, Hu QH, Zhu PF (2019) Fuzzy rough set based feature selection for large-scale Hierarchical classification. IEEE Trans Fuzzy Syst 27(10):1891–1903

    Article  Google Scholar 

  35. Zhang J, Kang DK, Silvescu A, Honavar V (2006) Learning accurate and concise naive Bayes classifiers from attribute value taxonomies and data. Knowl Inf Syst 9(2):157–179

    Article  Google Scholar 

  36. Zhang HY, Yang SY (2019) Three-way group decisions with interval-valued decision-theoretic rough sets based on aggregating inclusion measures. Int J Approx Reason 110:31–45

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. College of Science, Xi’an Shiyou University, Xi’an, 710065, China

    Xiaoli He & Yanhong She

  2. College of Computer Science, Xi’an Shiyou University, Xi’an, 710065, China

    Lin Zhao

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  1. Xiaoli He
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  2. Lin Zhao
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  3. Yanhong She
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Correspondence to Yanhong She.

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This work is supported by the National Nature Science Foundation of China (Nos. 12001422 and 61976244), Natural Science Basic Research Program of Shaanxi (Program No. 2021JQ580) and Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province (No. OBDMA202105).

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He, X., Zhao, L. & She, Y. On generalization reducts in incomplete multi-scale decision tables. Int. J. Mach. Learn. & Cyber. 15, 253–266 (2024). https://doi.org/10.1007/s13042-023-01906-6

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  • DOI: https://doi.org/10.1007/s13042-023-01906-6

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