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New uncertainty measurement for a decision table with application to feature selection

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Abstract

A decision table consists of samples, categorical features, and a decision feature. Uncertainty measurement (UM) can supply new points of view for analyzing data. Thus, it is vital to study the uncertainty of the decision table. Some UMs, such as classification precision, rough membership degree, dependence degree, and attribute importance, cannot accurately measure the uncertainty of a decision table. For example, the dependence degree only considers the information provided by the lower approximation of the decision and ignores the upper approximation, which may lead to some information loss. This paper proposes new UMs in a decision table and gives an application for feature selection. First, new UMs such as conditional information entropy, conditional information quantity, and conditional discriminant index in a decision table are proposed. Then, statistical analysis is used to identify the strengths and weaknesses of the proposed UMs. Next, the UM with the best performance is applied to create a heuristic select feature algorithm in a decision table. Finally, the created algorithm is compared to five other feature selection algorithms, and numerical experiments demonstrate its superior performance.

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The data used or analyzed during the current study are available from the corresponding author after the paper is accepted for publication.

References

  1. Li ZW, Zhang PF, Ge X, Xie NX, Zhang GQ, Wen CF (2019) Uncertainty measurement for a fuzzy relation information system. IEEE Trans Fuzzy Syst 27:2338–2352

    Google Scholar 

  2. Zeng AP, Li TR, Hu J, Chen HM, Luo C (2017) Dynamical updating fuzzy rough approximations for hybrid data under the variation of attribute values. Inf Sci 378:363–388

    MathSciNet  Google Scholar 

  3. Li ZW, Liu XF, Dai JH, Chen JL, Fujita H (2020) Measures of uncertainty based on Gaussian kernel for a fully fuzzy information system. Knowl-Based Syst 196:105791

    Google Scholar 

  4. Huang ZH, Li JJ (2022) Discernibility measures for fuzzy \(\beta \)-covering and their application. IEEE Transactions on Cybernetics 52(9):9722–9735

    Google Scholar 

  5. Dai JH, Wang WT, Xu Q (2013) An uncertainty measure for incomplete decision tables and its applications. IEEE Transactions on Cybernetics 43(4):1277–1289

    Google Scholar 

  6. Chen YM, Wu KS, Chen XH, Tang CH, Zhu QX (2014) An entropy-based uncertainty measurement approach in neighborhood systems. Inf Sci 279:239–250

    MathSciNet  Google Scholar 

  7. Wang XD, Song YF (2018) Uncertainty measure in evidence theory with its applications. Appl Intell 48:1672–1688

    Google Scholar 

  8. Zeng JS, Li ZW, Zhang PF, Wang P (2020) Information structures and uncertainty measures in a hybrid information system: Gaussian kernel method. Int J Fuzzy Syst 22:212–231

  9. Wang BL, Liang JY, Yao YY (2023) A trilevel analysis of uncertainty measuresin partition-based granular computing. Artif Intell Rev 56:533–575

    Google Scholar 

  10. Pawlak Z (1982) Rough sets. International Journal of Computer and Information Science 11:341–356

    Google Scholar 

  11. Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst 17(2–3):191–209

    Google Scholar 

  12. Wang XZ, Tsang ECC, Zhao SY, Chen DG, Yeung DS (2007) Learning fuzzy rules from fuzzy samples based on rough set technique. Inf Sci 177:4493–4514

    MathSciNet  Google Scholar 

  13. Jia XY, Li WW, Shang L (2019) A multiphase cost-sensitive learning method based on the multiclass three-way decision-theoretic rough set model. Inf Sci 485:248–262

    Google Scholar 

  14. Wang YB, Chen XJ, Dong K (2019) Attribute reduction via local conditional entropy. Int J Mach Learn Cybern 10(12):3619–3634

    Google Scholar 

  15. Zhang PF, Li TR, Yuan Z, Luo C, Liu K, Yang X (2022) Heterogeneous feature selection based on neighborhood combination entropy. IEEE transactions on neural networks and Learning Systerm. https://doi.org/10.1109/TNNLS.2022.3193929

    Article  Google Scholar 

  16. Shannon C (1948) A mathematical theory of communication. The Bell System Technical Journal 27:379–423

    MathSciNet  Google Scholar 

  17. Cament LA, Castillo LE, Perez JP, Galdames FJ, Perez CA (2014) Fusion of local normalization and Gabor entropy weighted features for face identification. Pattern Recogn 47(2):568–577

    Google Scholar 

  18. Hempelmann CF, Sakoglu U, Gurupur VP, Jampana S (2016) An entropy-based evaluation method for knowledge bases of medical information systems. Expert Syst Appl 46:262–273

    Google Scholar 

  19. Tan AH, Shi SW, Wu WZ, Li JJ, Pedrycz W (2022) Granularity and entropy of intuitionistic fuzzy information and their applications. IEEE Transactions on Cybernetics 52(1):192–204

    Google Scholar 

  20. Navarrete J, Viejo D, Cazorla M (2016) Color smoothing for RGB-D data using entropy information. Appl Soft Comput 46:361–380

    Google Scholar 

  21. Wan L, Xia SJ, Zhu Y, Lyu ZH (2021) An improved semi-supervised feature selection algorithm based on information entropy. Statistics & Decision 17:66–70

    Google Scholar 

  22. Wan J, Chen H, Yuan Z, Li T, Yang X, Sang B (2021) A novel hybrid feature selection method considering feature interaction in neighborhood rough set. Knowl-Based Syst 227:107167

    Google Scholar 

  23. Cornelis C, Jensen R, Martin GH, Slezak D (2010) Attribute selection with fuzzy decision reducts. Inf Sci 180:209–224

    MathSciNet  Google Scholar 

  24. Dai JH, Hu QH, Zhang JH, Hu H, Zheng NG (2017) Attribute selection for partially labeled categorical data by rough set approach. IEEE Transactions on Cybernetics 47(9):2460–2471

    Google Scholar 

  25. Wang C, Wang Y, Shao M, Qian Y, Chen D (2020) Fuzzy rough attribute reduction for categorical data. IEEE Trans Fuzzy Syst 28(5):818–830

    Google Scholar 

  26. Chen LL, Chen DG, Wang H (2019) Fuzzy kernel alignment with application to attribute reduction of heterogeneous data. IEEE Trans Fuzzy Syst 27:1469–1478

    Google Scholar 

  27. Liu GL, Feng YB, Yang JT (2020) A common attribute reduction form for information systems. Knowl-Based Syst 193:105466

    Google Scholar 

  28. Jain P, Tiwari AK, Som T (2020) A fitting model based intuitionistic fuzzy rough feature selection. Eng Appl Artif Intell 89:103421

    Google Scholar 

  29. Liu KY, Yang XB, Yu HL, Mi JS (2019) Rough set based semi-supervised feature selection via ensemble selector. Knowl-Based Syst 165:282–296

    Google Scholar 

  30. Wu XP, Chen HM, Li TR, Wan JH (2021) Semi-supervised feature selection with minimal redundancy based on local adaptive. Appl Intell 51:8542–8563

    Google Scholar 

  31. Wan JH, Chen HM, Yuan Z, Li TR, Yang XL, Sang BB (2021) A novel hybrid feature selection method considering feature interaction in neighborhood rough set. Knowl-Based Syst 227:107–167

  32. Zhang PF, Li TR, Yuan Z, Luo C, Wang GQ, Liu J, Du SD (2022) A data-level fusion model for unsupervised attribute selection in multi-source homogeneous data. Information Fusion 80:87–103

    Google Scholar 

  33. Yin TY, Chen HM, Yuan Z, Wan JH, Liu KY, Horng SJ, Li TR (2023) A robust multilabel feature selection approach based on graph structure considering fuzzy dependency and feature interaction. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2023.3287193

    Article  Google Scholar 

  34. Wang CZ, Huang Y, Shao MW, Hu QH, Chen DG (2020) Feature selection based on neighborhood self-information. IEEE Transactions on Cybernetics 50(9):4031–4042

    Google Scholar 

  35. Zhang QL, Qu LD, Li ZW (2022) Attribute reduction based on D-S evidence theory in a hybrid information system. Int J Approximate Reasoning 148:202–234

    MathSciNet  Google Scholar 

  36. Yin TY, Chen HM, Yuan Z, Li TR, Liu KY (2022) Noise-resistant multilabel fuzzy neighborhood rough sets for feature subset selection. Inf Sci 621:200–226

    Google Scholar 

  37. Zhang PF, Li TR, Yuan Z, Deng ZX, Wang GQ, Wang DX, Zhang F (2023) A possibilistic information fusion-based unsupervised feature selection method using information quality measures. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2023.3238803

    Article  Google Scholar 

  38. Wang GY, Yu H, Yang DC (2002) Decision table reduction based on conditional information entropy. Chinese Computers 25(7):759–766

    MathSciNet  Google Scholar 

  39. Yuan XJ, Zhang WX (2003) Studies on equivalence of the distribution reduction and the strictly convex function based reduction in decision tables. Syst Eng 21(5):5–7

    Google Scholar 

  40. Tiwari A, Chaturvedi A (2022) A hybrid feature selection approach based on information theory and dynamic butterfly optimization algorithm for data classification. Expert Syst Appl 196:116621

    Google Scholar 

  41. Wang CZ, Wang Y, Shao MW, Qian YH, Chen DG (2020) Fuzzy rough attribute reduction for categorical data. IEEE Trans Fuzzy Syst 28(5):818–830

    Google Scholar 

  42. Hu M, Tsang ECC, Guo YT, Xu WH (2022) Fast and robust attribute reduction based on the separability in fuzzy decision systems. IEEE Transactions on Cybernetics 52(6):5559–5572

    Google Scholar 

  43. Wang CZ, Hu Q, Wang X, Chen D, Qian Y, Dong Z (2018) Feature selection based on neighborhood discrimination index. IEEE Transactions on Neural Networks and Learning Systems 29(7):2986–2999

    MathSciNet  Google Scholar 

  44. Luo C, Wang S, Li T, Chen H, Lv JC, Zhang Y (2023) Spark rough hypercuboid approach for scalable feature selection. IEEE Trans Knowl Data Eng 35(3):3130–3144

    Google Scholar 

  45. Kryszkiewicz M (1999) Rules in incomplete information systems. Inf Sci 113:271–292

    MathSciNet  Google Scholar 

  46. Zhang GQ, Li ZW, Wu WZ, Liu XF, Xie NX (2018) Information structures and uncertainty measures in a fully fuzzy information system. Int J Approximate Reasoning 101:119–149

    MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to thank the editors and the anonymous reviewers for their valuable comments and suggestions, which have helped immensely in improving the quality of the paper. This work is supported by the Natural Science Foundation of Guangxi Province (2021GXNSFAA220114), the Key Laboratory of Software Engineering in Guangxi Minzu University (2022-18XJSY-03), and Research Fund of Guangxi Key Lab of Multi-source Information Mining & Security (MIMS19-M-02).

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Authors and Affiliations

  1. School of Artificial Intelligence, Guangxi Minzu University, Nanning, Guangxi, 530006, People’s Republic of China

    Gangqiang Zhang

  2. Center for Applied Mathematics of Guangxi, Key Laboratory of Complex System Optimization and Big Data Processing in Department of Guangxi Education, Yulin Normal University, Yulin, Guangxi, 537000, People’s Republic of China

    Yan Song

  3. School of Big Data and Artificial Intelligence, Guangxi University of Finance and Economics, Nanning, Guangxi, 530003, People’s Republic of China

    Guangji Yu

  4. Fujian Key Laboratory of Financial Information Processing, Key Laboratory of Applied Mathematics in Fujian Province University, Putian University, Putian, Fujian, 351100, People’s Republic of China

    Zhaowen Li

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  1. Gangqiang Zhang
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  2. Yan Song
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  4. Zhaowen Li
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Contributions

Gangqiang Zhang: Methodology, Writing-Original draft; Yan Song: Software, Editing, Investigation; Guangji Yu: Software, Investigation; Zhaowen Li: Validation, Editing.

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Correspondence to Yan Song or Zhaowen Li.

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Zhang, G., Song, Y., Yu, G. et al. New uncertainty measurement for a decision table with application to feature selection. Appl Intell 54, 3092–3118 (2024). https://doi.org/10.1007/s10489-024-05310-7

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