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Attribute reduction based on the Boolean matrix

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Abstract

Attribute reduction is an important preprocessing step in machine learning and pattern recognition. This paper introduces condition-attribute Boolean matrix and decision-attribute Boolean matrix and proposes a new attribute reduction model based on Boolean operations according to the concept of neighborhood rough set. Some operation rules of Boolean vectors are defined and an uncertainty measure, named attribute support function, is proposed to evaluate the importance degree of candidate attributes with respect to decision attributes. An attribute reduction algorithm based on the proposed measure is designed. Ten data sets selected from public data sources are used to compare the proposed algorithm with some existing algorithms. The experimental results show that the proposed reduction algorithm is feasible and effective.

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References

  • An S, Shi H, Hu Q, Li X, Dang J-W (2014) Fuzzy rough regression with application to wind speed prediction. Inf Sci 282:388–400

    Article  MathSciNet  Google Scholar 

  • An S, Hu Q, Pedrycz W, Zhu P, Eric C, Tsang C (2016) Data-distribution-aware fuzzy rough set model and its application to robust classification. IEEE Trans Cybern 46(12):3073–3085

    Google Scholar 

  • Chen D, Zhang L, Zhao S, Hu Q, Zhu P (2013) A novel algorithm for finding reducts with fuzzy rough sets. IEEE Trans Fuzzy Syst 20(2):385–389

    Article  Google Scholar 

  • Chen Y, Zhang Z, Zheng J, Ma Y, Xue Y (2017) Gene selection for tumor classification using neighborhood rough sets and entropy measures. J Biomed Inform 67:59–68

    Article  Google Scholar 

  • Dai J, Xu Q (2013) Attribute selection based on information gain ratio in fuzzy rough set theory with application to tumor classification. Appl Soft Comput 13(1):211–221

    Article  Google Scholar 

  • Dai J, Hu H, Wu W, Qian Y, Huang D (2017) Maximal discernibility pairs based approach to attribute reduction in fuzzy rough sets. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2017.2768044

    Article  Google Scholar 

  • Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst 17:191–208

    Article  MATH  Google Scholar 

  • Greco S, Matarazzo B, Slowinski R (2002) Rough approximation by dominance relations. Int J Intell Syst 17:153–171

    Article  MATH  Google Scholar 

  • Hu Q, Yu D, Liu J, Wu C (2008) Neighborhood-rough-set based heterogeneous feature subset selection. Inf Sci 178(18):3577–3594

    Article  MathSciNet  MATH  Google Scholar 

  • Huang B, Li H (2018) Distance-based information granularity in neighborhood-based granular space. Granul Comput 3(2):93–110

    Article  Google Scholar 

  • Huang B, Guo C, Zhuang Y, Li H, Zhou X (2014) Intuitionistic fuzzy multi-granulation rough sets. Inf Sci 277:299–320

    Article  MATH  Google Scholar 

  • Kim D (2001) Data classification based on tolerant rough set. Pattern Recogn 34(8):1613–1624

    Article  MATH  Google Scholar 

  • Lang G, Li Q, Cai M, Yang T, Xiao Q (2017a) Incremental approaches to knowledge reduction based on characteristic matrices. Int J Mach Learn Cybern 8(1):203–222

    Article  Google Scholar 

  • Lang G, Miao D, Cai M, Zhang Z (2017b) Incremental approaches for updating reducts in dynamic covering information systems. Knowl Based Syst 134:85–104

    Article  Google Scholar 

  • Li J, Ren Y, Mei C, Qian Y, Yang X (2016) A comparative study of multigranulation rough sets and concept lattices via rule acquisition. Knowl Based Syst 91:152–164

    Article  Google Scholar 

  • Li J, Aswani Kumar C, Mei C, Wang X (2017) Comparison of reduction in formal decision contexts. Int J Approx Reason 80:100–122

    Article  MathSciNet  MATH  Google Scholar 

  • Liang J, Wang F, Dang C, Qian Y (2014) A group incremental approach to attribute selection applying rough set technique. IEEE Trans Knowl Data Eng 26(2):294–304

    Article  Google Scholar 

  • Lin T (1997) Neighborhood systems: application to qualitative fuzzy and rough sets. In: Wang PP (ed) Advances in machine intelligence and soft computing. Department of Electrical Engineering, Duke University, Durham, pp 132–155

    Google Scholar 

  • Lin Y, Hu Q, Liu J, Li J, Wu X (2017) Streaming feature selection for multi-label learning based on fuzzy mutual information. IEEE Trans Fuzzy Syst 25(6):1491–1507

    Article  Google Scholar 

  • Liu H, Gegov A, Cocea M (2016) Rule-based systems: a granular computing perspective. Granul Comput 1(4):259–274

    Article  Google Scholar 

  • Mandal P, Ranadive AS (2018) Multi-granulation interval-valued fuzzy probabilistic rough sets and their corresponding three-way decisions based on interval-valued fuzzy preference relations. Granul Comput. https://doi.org/10.1007/s41066-018-0090-9

    Article  MATH  Google Scholar 

  • Min F, Zhu W (2012) Attribute reduction of data with error ranges and test costs. Inf Sci 211:48–67

    Article  MathSciNet  MATH  Google Scholar 

  • Pawlak Z (1982) Rough sets. Int J Comput Inform Sci 11(5):341–356

    Article  MATH  Google Scholar 

  • Pawlak Z, Skowron A (2006) Rudiments of rough sets. Inf Sci 177:3–27

    Article  MathSciNet  MATH  Google Scholar 

  • Pedrycz W, Chen S (2011) Granular computing and intelligent systems: design with information granules of high order and high type. Springer, Heidelberg

    Book  Google Scholar 

  • Pedrycz W, Chen S (2015a) Granular computing and decision-making: interactive and iterative approaches. Springer, Heidelberg

    Book  Google Scholar 

  • Pedrycz W, Chen S (2015b) Information granularity, big data, and computational intelligence. Springer, Heidelberg

    Book  Google Scholar 

  • Qian Y, Liang J, Yao Y, Dang C (2010) MGRS: a multi-granulation rough set. Inf Sci 180:949–970

    Article  MathSciNet  MATH  Google Scholar 

  • Qian Y, Liang J, Pedrycz W, Dang C (2011) An efficient accelerator for attribute reduction from incomplete data in rough set framework. Pattern Recogn 44(8):1658–1670

    Article  MATH  Google Scholar 

  • She Y, He X, Ma L (2017a) On the structure of metric spaces related to pre-rough logic. Int J Mach Learn Cybern 8(2):537–546

    Article  Google Scholar 

  • She Y, He X, Shi H, Qian Y (2017b) A multiple-valued logic approach for multigranulation rough set model. Int J Approx Reason 82:270–284

    Article  MathSciNet  MATH  Google Scholar 

  • Sun L, Xu J, Tian Y (2012) Feature selection using rough entropy-based uncertainty measures in incomplete decision systems. Knowl Based Syst 36:206–216

    Article  Google Scholar 

  • Sun B, Ma W, Chen X (2015) Fuzzy rough set on probabilistic approximation space over two universes and its application to emergency decision-making. Expert Syst 32(4):507–521

    Article  Google Scholar 

  • Sun B, Ma W, Qian Y (2017) Multi-granulation fuzzy rough set over two universes and its application to decision making. Knowl Based Syst 123:61–74

    Article  Google Scholar 

  • Wang B, Liang J, Qian Y (2014) Determining decision makers’ weights in group ranking: a granular computing method. Int J Mach Learn Cybern 6(3):511–521

    Article  Google Scholar 

  • Wang C, Qi Y, Shao Y et al (2016a) A fitting model for feature selection with fuzzy rough sets. IEEE Trans Fuzzy Syst 25(4):741–753

    Article  Google Scholar 

  • Wang C, Shao M, He Q, Qian Y, Qi Y (2016b) Feature subset selection based on fuzzy neighborhood rough sets. Knowl Based Syst 111(1):173–179

    Article  Google Scholar 

  • Wang C, Hu Q, Wang X, Chen D, Qian Y (2017a) Feature selection based on neighborhood discrimination index. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2710422

    Article  Google Scholar 

  • Wang C, He Q, Shao M, Xua Y, Hu Q (2017b) A unified information measure for general binary relations. Knowl Based Syst 135(1):18–28

    Article  Google Scholar 

  • Wang G, Li Y, Li X (2017c) Approximation performance of the nonlinear hybrid fuzzy system based on variable universe. Granul Comput 2:1–12

    Article  Google Scholar 

  • Wang G, Yang J, Xu J (2017d) Granular computing: from granularity optimization to multi-granularity joint problem solving. Granul Comput 2:1–16

    Article  Google Scholar 

  • Wang C, He Q, Shao M, Hu Q (2018) Feature selection based on maximal neighborhood discernibility. Int J Mach Learn Cybern. https://doi.org/10.1007/s13042-017-0712-6

    Article  Google Scholar 

  • Wu W, Zhang W (2002) Neighborhood operator systems and approximations. Inf Sci 144(14):201–217

    Article  MathSciNet  MATH  Google Scholar 

  • Xu W, Li W (2016a) Granular computing approach to two-way learning based on formal concept analysis in fuzzy datasets. IEEE Trans Cybern 46(2):366–379

    Article  MathSciNet  Google Scholar 

  • Xu Z, Wang H (2016b) Managing multi-granularity linguistic information in qualitative group decision making: an overview. Granul Comput 1(1):21–35

    Article  Google Scholar 

  • Xu W, Yu J (2017a) A novel approach to information fusion in multi-source datasets: a granular computing viewpoint. Inf Sci 378:410–423

    Article  Google Scholar 

  • Xu W, Li W, Zhang X (2017b) Generalized multigranulation rough sets and optimal granularity selection. Granul Comput 4(2):271–288

    Article  Google Scholar 

  • Yang X, Qi Y, Yu D, Yu H, Yang J (2015) α-Dominance relation and rough sets in interval-valued information systems. Inf Sci 294:334–347

    Article  MathSciNet  MATH  Google Scholar 

  • Yang Y, Chen D, Wang H, Eric C, Tsang C, Zhang D (2017a) Fuzzy rough set based incremental attribute reduction from dynamic data with sample arriving. Fuzzy Sets Syst 312:66–86

    Article  MathSciNet  MATH  Google Scholar 

  • Yang Y, Chen D, Wang H (2017b) Active sample selection based incremental algorithm for attribute reduction with rough sets. IEEE Trans Fuzzy Systems 25(4):825–838

    Article  Google Scholar 

  • Yao Y (1998) Relational interpretations of neighborhood operators and rough set approximation operators. Inf Sci 101:239–259

    Article  MathSciNet  MATH  Google Scholar 

  • Yao Y, Mi J, Li Z (2011) Attribute reduction based on generalized fuzzy evidence theory in fuzzy decision systems. Fuzzy Sets Syst 170(1):64–75

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang H, Yang S (2016) Inclusion measure for typical hesitant fuzzy sets, the relative similarity measure and fuzzy entropy. Soft Comput 20(4):1277–1287

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang H, Yang S (2017) Feature selection and approximate reasoning of large-scale set-valued decision tables based on alpha-dominance-based quantitative rough sets. Inf Sci 378:328–347

    Article  Google Scholar 

  • Zhang X, Zhou B, Li P (2012) A general frame for intuitionistic fuzzy rough sets. Inf Sci 216:34–49

    Article  MathSciNet  MATH  Google Scholar 

  • Zhao S, Tsang C, Chen D (2010) Building a rule-based classifier by using fuzzy rough set technique. IEEE Trans Knowl Data Eng 22(5):624–638

    Article  Google Scholar 

  • Zhao S, Chen H, Li C, Du X, Sun H (2015) A novel approach to building a robust fuzzy rough classifier. IEEE Trans Fuzzy Syst 23(4):769–786

    Article  Google Scholar 

  • Zhao H, Wang P, Hu Q (2016) Cost-sensitive feature selection based on adaptive neighborhood granularity with multi-level confidence. Inf Sci 366:134–149

    Article  MathSciNet  Google Scholar 

  • Zhu P, Hu Q (2013) Adaptive neighborhood granularity selection and combination based on margin distribution optimization. Inf Sci 249:1–12

    Article  MathSciNet  MATH  Google Scholar 

  • Zhu W, Wang F (2007) On three types of covering-based rough sets. IEEE Trans Knowl Data Eng 19(8):1131–1144

    Article  Google Scholar 

  • Ziarko W (1993) Variable precision rough sets model. J Comput Syst Sci 46:139–159

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants 61572082, 61673396, and 61473111, the Foundation of Educational Committee of Liaoning Province (LZ2016003), and the Natural Science Foundation of Liaoning Province (20170540012, 20170540004).

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Authors and Affiliations

  1. Department of Mathematics, Bohai University, Jinzhou, 121000, People’s Republic of China

    Yunpeng Shi, Yang Huang & Changzhong Wang

  2. College of Science, Beijing University of Civil Engineering and Architecture, Beijing, 100044, People’s Republic of China

    Qiang He

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  1. Yunpeng Shi
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  2. Yang Huang
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  3. Changzhong Wang
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  4. Qiang He
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Correspondence to Changzhong Wang.

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Shi, Y., Huang, Y., Wang, C. et al. Attribute reduction based on the Boolean matrix. Granul. Comput. 4, 313–322 (2019). https://doi.org/10.1007/s41066-018-0108-3

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