Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Attribute reduction based on interval-set rough sets

  • Foundation, algebraic, and analytical methods in soft computing
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

As an important extension of the rough set theory, interval-set rough sets provide an effective method to solve the problem that the objective sets cannot be accurately expressed in the rough approximation process and to induce classification rules from incomplete information systems. In practical information systems, the value of an object’s decision attribute may be set-valued due to missing decision information or multiple decision values. However, this situation is not considered by any of the existing rough set models. Therefore, to properly deal with the information system where decision attributes are set-valued, we construct the interval-set rough set model on the information system and study attribute reductions of interval-set rough sets. First, we define the information system where decision attributes are set-valued as an extended set-valued decision information system (ESVDIS) and construct the interval-set rough set model on the ESVDIS. Second, the accuracy and the roughness are extended to the interval-set approximation accuracy and the interval-set approximation roughness, respectively. The two extended measures can be used to measure the uncertainty caused by rough approximations. In addition, the dependency degree of interval-set rough sets called the interval-set dependency degree is defined to estimate the significance of attribute subsets. By adopting the interval-set dependency degree, we propose the definition of attribute reduction based on interval-set rough sets and design a heuristic attribute reduction algorithm. Finally, the effectiveness of the proposed attribute reduction algorithm is demonstrated using 12 public data sets. Experimental results show that the model is applicable to some fields, such as missing decision information and group decision-making.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Algorithm 1
Fig. 1
Fig. 2

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Availability of data and materials

Not applicable.

Code Availability

Not applicable.

References

  • Abo-Tabl E (2011) A comparison of two kinds of definitions of rough approximations based on a similarity relation. Inf Sci 181(12):2587–2596

    Article  MathSciNet  Google Scholar 

  • An S, Guo X, Wang C et al (2023a) A soft neighborhood rough set model and its applications. Inf Sci 624:185–199

    Article  Google Scholar 

  • An S, Zhang M, Wang C et al (2023b) Robust fuzzy rough approximations with KNN granules for semi-supervised feature selection. Fuzzy Sets Syst 461:108476

    Article  MathSciNet  Google Scholar 

  • Asuncion A, Newman D (2007) UCI machine learning repository. https://archive.ics.uci.edu/ml

  • Boukezzoula R, Jaulin L, Desrochers B et al (2020) Thick fuzzy sets (TFSS) and their potential use in uncertain fuzzy computations and modeling. IEEE Trans Fuzzy Syst 29(11):3334–3348

    Article  Google Scholar 

  • Chu X, Sun B, Li X et al (2020) Neighborhood rough set-based three-way clustering considering attribute correlations: an approach to classification of potential gout groups. Inf Sci 535:28–41

    Article  MathSciNet  Google Scholar 

  • Dai J, Tian H (2013) Entropy measures and granularity measures for set-valued information systems. Inf Sci 240:72–82

    Article  MathSciNet  Google Scholar 

  • Dai J, Gao S, Zheng G (2018) Generalized rough set models determined by multiple neighborhoods generated from a similarity relation. Soft Comput 22:2081–2094

    Article  Google Scholar 

  • Desrochers B, Jaulin L (2017) Thick set inversion. Artif Intell 249:1–18

    Article  MathSciNet  Google Scholar 

  • Gong ZT, Sun BZ, Chen DG (2008) Rough set theory for the interval-valued fuzzy information systems. Inf Sci 178(8):1968–1985

    Article  MathSciNet  Google Scholar 

  • Guan YY, Wang HK (2006) Set-valued information systems. Inf Sci 176(17):2507–2525

    Article  MathSciNet  Google Scholar 

  • Guo YT, Hu M, Wang XZ et al (2022) A robust approach to attribute reduction based on double fuzzy consistency measure. Knowl-Based Syst 253:109585

    Article  Google Scholar 

  • Gupta A, Begum SA (2023) Fuzzy rough set-based feature selection for text categorization. Fuzzy, rough and intuitionistic fuzzy set approaches for data handling, theory and applications. Springer, Berlin, pp 65–85

    Chapter  Google Scholar 

  • Hota R, Dash S, Mishra S et al (2023) Prediction and diagnosis of thoracic diseases using rough set and machine learning. In: 2023 10th International conference on computing for sustainable global development (INDIACom). IEEE, pp 206–213

  • Hu BQ (2013) Three decisions rough sets based on interval sets. Three decisions and granular computering (in Chinese). Science Press, Beijing, pp 163–195

    Google Scholar 

  • Hu M (2023) Modeling relationships in three-way conflict analysis with subsethood measures. Knowl-Based Syst 260:110131

    Article  Google Scholar 

  • Hu M, Tsang EC, Guo YT et al (2021) A novel approach to attribute reduction based on weighted neighborhood rough sets. Knowl-Based Syst 220:106908

    Article  Google Scholar 

  • Huang YY, Li TR, Luo C et al (2017) Dynamic variable precision rough set approach for probabilistic set-valued information systems. Knowl-Based Syst 122:131–147

    Article  Google Scholar 

  • Huang QQ, Li TR, Huang YY et al (2020) Dynamic dominance rough set approach for processing composite ordered data. Knowl-Based Syst 187:104829

    Article  Google Scholar 

  • Jaura S, Ramanna S (2023) Named entity recognition on cord-19 bio-medical dataset with tolerance rough sets. Transactions on rough sets XXIII. Springer, Berlin, pp 23–32

    Google Scholar 

  • Ji X, Peng JH, Zhao P et al (2023) Extended rough sets model based on fuzzy granular ball and its attribute reduction. Inf Sci 640:119071

    Article  Google Scholar 

  • Jiang HB, Zhan JM, Sun BZ et al (2020a) An MADM approach to covering-based variable precision fuzzy rough sets: an application to medical diagnosis. Int J Mach Learn Cybern 11:2181–2207

    Article  Google Scholar 

  • Jiang ZH, Liu KY, Yang XB et al (2020b) Accelerator for supervised neighborhood based attribute reduction. Int J Approx Reason 119:122–150

    Article  MathSciNet  Google Scholar 

  • Jiang H, Wang G, Liu Q et al (2023) Hierarchical multi-UAVS task assignment based on dominance rough sets. Appl Soft Comput 143:110445

    Article  Google Scholar 

  • Li HX, Wang MH, Zhou XZ et al (2012) An interval set model for learning rules from incomplete information table. Int J Approx Reason 53(1):24–37

    Article  MathSciNet  Google Scholar 

  • Liu J, Lin Y, Du J et al (2023) Asfs: a novel streaming feature selection for multi-label data based on neighborhood rough set. Appl Intell 53(2):1707–1724

    Article  Google Scholar 

  • Ma JM, Jing Y, Yao HJ (2018) The monotonicity of interval-set probabilistic rough sets. Fuzzy Syst Math 32(4):180–190 (in Chinese)

    Google Scholar 

  • Mac Parthalain N, Shen Q (2009) Exploring the boundary region of tolerance rough sets for feature selection. Pattern Recogn 42(5):655–667

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data, vol 9. Springer Science & Business Media, Heidelberg

    Book  Google Scholar 

  • Qian YH, Dang CY, Liang JY et al (2009) Set-valued ordered information systems. Inf Sci 179(16):2809–2832

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Raja P, Thangavel K (2020) Missing value imputation using unsupervised machine learning techniques. Soft Comput 24(6):4361–4392

    Article  Google Scholar 

  • Sun BZ, Chen XT, Zhang LY et al (2020) Three-way decision making approach to conflict analysis and resolution using probabilistic rough set over two universes. Inf Sci 507:809–822

    Article  MathSciNet  Google Scholar 

  • Wang CZ, Hu QH, Wang XZ et al (2017) Feature selection based on neighborhood discrimination index. IEEE Trans Neural Netw Learn Syst 29(7):2986–2999

    MathSciNet  Google Scholar 

  • Wang CZ, Huang Y, Shao MW et al (2019a) Uncertainty measures for general fuzzy relations. Fuzzy Sets Syst 360:82–96

    Article  MathSciNet  Google Scholar 

  • Wang CZ, Huang Y, Shao MW et al (2019b) Fuzzy rough set-based attribute reduction using distance measures. Knowl-Based Syst 164:205–212

    Article  Google Scholar 

  • Wang P, Zhang PF, Li ZW (2019c) A three-way decision method based on gaussian kernel in a hybrid information system with images: an application in medical diagnosis. Appl Soft Comput 77:734–749

  • Wilcoxon F (1992) Individual comparisons by ranking methods. Breakthroughs in statistics: methodology and distribution. Springer, New York, pp 196–202

    Chapter  Google Scholar 

  • Xie LL, Lin GP, Li JJ et al (2023) Local fuzzy rough set model over two universes and its reduction. Soft Comput 1–19

  • Xie G, Zhang JL, Lai KK et al (2008) Variable precision rough set for group decision-making: an application. Int J Approx Reason 49(2):331–343

    Article  Google Scholar 

  • Xu JC, Meng XR, Qu KL et al (2023) Feature selection using relative dependency complement mutual information in fitting fuzzy rough set model. Appl Intell 53:18239–18262

    Article  Google Scholar 

  • Yao YY, Noroozi N (1994) A unified model for set-based computations. In: Soft computing: 3rd international workshop on rough sets and soft computing, Citeseer, pp 252–255

  • Yao YY (1993) Interval-set algebra for qualitative knowledge representation. In: Proceedings of ICCI’93: 5th international conference on computing and information. IEEE, pp 370–374

  • Yao YY (1996) Two views of the theory of rough sets in finite universes. Int J Approx Reason 15(4):291–317

    Article  MathSciNet  Google Scholar 

  • Yao YY (2001) Information granulation and rough set approximation. Int J Intell Syst 16(1):87–104

    Article  MathSciNet  Google Scholar 

  • Yin T, Chen H, Yuan Z et al (2023a) Noise-resistant multilabel fuzzy neighborhood rough sets for feature subset selection. Inf Sci 621:200–226

    Article  Google Scholar 

  • Yin T, Chen H, Yuan Z et al (2023b) A robust multilabel feature selection approach based on graph structure considering fuzzy dependency and feature interaction. IEEE Trans Fuzzy Syst 31:4516–4523

    Article  Google Scholar 

  • Zhang JB, Li TR, Ruan D et al (2012) Rough sets based matrix approaches with dynamic attribute variation in set-valued information systems. Int J Approx Reason 53(4):620–635

    Article  MathSciNet  Google Scholar 

  • Zhang YM, Jia XY, Tang ZM (2021) Information-theoretic measures of uncertainty for interval-set decision tables. Inf Sci 577:81–104

    Article  MathSciNet  Google Scholar 

  • Zhao XR, Hu BQ (2015) Fuzzy and interval-valued fuzzy decision-theoretic rough set approaches based on fuzzy probability measure. Inf Sci 298:534–554

    Article  MathSciNet  Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China under Grant No. 62172048.

Author information

Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Chunge Ren & Ping Zhu

  2. Key Laboratory of Mathematics and Information Networks (Beijing University of Posts and Telecommunications), Ministry of Education, Beijing, China

    Ping Zhu

Authors
  1. Chunge Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ping Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ping Zhu.

Ethics declarations

Conflict of interest

The authors declare no conflicts of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ren, C., Zhu, P. Attribute reduction based on interval-set rough sets. Soft Comput 28, 1893–1908 (2024). https://doi.org/10.1007/s00500-023-09540-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-023-09540-8

Keywords