SpringerLink
Log in

An interpretable hypersphere information granule-based classifier for numeric data using axiomatic fuzzy set

  • Original Paper
  • Published:
Granular Computing Aims and scope Submit manuscript

Abstract

The interpretability of classifiers focused on numerical data continues to pose significant challenges. This paper introduces an interpretable classifier rooted in axiomatic fuzzy set (AFS) theory and granular computing (GrC). The design of the proposed classifier consists of three stages: the construction of hypersphere information granules, the optimization of hypersphere information granules, and finding the semantic description of hypersphere information granules by applying AFS theory. The resulting classifier leverages hypersphere information granules to capture the data’s structural characteristics while facilitating the semantic interpretation of the overall structural landscape. Comprehensive evaluation across 17 diverse datasets demonstrates that the proposed classifier achieves better classification accuracy and interpretability.

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
EUR 32.99 /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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data availability

No datasets were generated or analyzed during the current study.

References

  • Alfeo AL, Cimino MG, Gagliardi G (2023) Concept-wise granular computing for explainable artificial intelligence. Granul Comput 8(4):827–838

    Article  Google Scholar 

  • Almeida LB (2020) Multilayer perceptrons. In: Handbook of neural computation. CRC Press, pp C1–C2

  • Bastos JA, Caiado J (2021) On the classification of financial data with domain agnostic features. Int J Approx Reason 138:1–11

    Article  MathSciNet  Google Scholar 

  • Bernardo J, Berger J, Dawid A et al (1998) Regression and classification using Gaussian process priors. Bayesian Stat 6:475

    Google Scholar 

  • Bezdek JC, Ehrlich R, Full W (1984) Fcm: the fuzzy c-means clustering algorithm. Comput Geosci 10(2–3):191–203

    Article  Google Scholar 

  • Breiman L (2001) Random forests. Mach Learn 45:5–32

    Article  Google Scholar 

  • Chen SM, Lee LW (2010) Fuzzy decision-making based on likelihood-based comparison relations. IEEE Trans Fuzzy Syst 18(3):613–628

    Article  Google Scholar 

  • Chen SM, Niou SJ (2011) Fuzzy multiple attributes group decision-making based on fuzzy preference relations. Expert Syst Appl 38(4):3865–3872

    Article  Google Scholar 

  • Chen SM, Wang JY (1995) Document retrieval using knowledge-based fuzzy information retrieval techniques. IEEE Trans Syst Man Cybern 25(5):793–803

    Article  Google Scholar 

  • Chen SM, Wang NY (2010) Fuzzy forecasting based on fuzzy-trend logical relationship groups. IEEE Trans Syst Man Cybern Part B (Cybern) 40(5):1343–1358

    Article  Google Scholar 

  • Chen SM, Ko YK, Chang YC et al (2009) Weighted fuzzy interpolative reasoning based on weighted increment transformation and weighted ratio transformation techniques. IEEE Trans Fuzzy Syst 17(6):1412–1427

    Article  Google Scholar 

  • Chen D, Xu W, Li J (2019) Granular computing in machine learning. Granul Comput 4:299–300

    Article  Google Scholar 

  • Cover T, Hart P (1967) Nearest neighbor pattern classification. IEEE Trans Inf Theory 13(1):21–27

    Article  Google Scholar 

  • De Ville B (2013) Decision trees. Wiley Interdiscip Rev Comput Stat 5(6):448–455

    Article  Google Scholar 

  • Deng Y, Liu X, **n C et al (2019) An interpretable classifier with linear discriminant analysis based on AFS theory. In: 2019 Chinese Control Conference (CCC). IEEE, pp 7583–7588

  • Dogan A, Birant D (2021) Machine learning and data mining in manufacturing. Expert Syst Appl 166:114060

    Article  Google Scholar 

  • Feng X, Liu X, Yaqing L (2014) Fuzzy classification algorithm based on fuzzy concept similarity and fuzzy entropy measure. J Dalian Univ Technol 54(2):240–245

    Google Scholar 

  • Fix E, Hodges JL (1989) Discriminatory analysis: nonparametric discrimination: consistency properties. Int Stat Rev Revue/Internationale de Statistique 57(3):238–247

    Article  Google Scholar 

  • Fu C, Lu W, Pedrycz W et al (2019) Fuzzy granular classification based on the principle of justifiable granularity. Knowl-Based Syst 170:89–101

    Article  Google Scholar 

  • Fu C, Lu W, Pedrycz W et al (2020) Rule-based granular classification: a hypersphere information granule-based method. Knowl-Based Syst 194:105500

    Article  Google Scholar 

  • Ho TK (1995) Random decision forests. In: Proceedings of 3rd international conference on document analysis and recognition. IEEE, pp 278–282

  • Jia W, Liu X, Wang Y et al (2022) Semisupervised learning via axiomatic fuzzy set theory and SVM. IEEE Trans Cybern 52(6):4661–4674

    Article  Google Scholar 

  • Kamiński B, Jakubczyk M, Szufel P (2018) A framework for sensitivity analysis of decision trees. CEJOR 26:135–159

    Article  MathSciNet  Google Scholar 

  • Kotsiantis SB (2013) Decision trees: a recent overview. Artif Intell Rev 39:261–283

    Article  Google Scholar 

  • Li Z, Wang C, Liu X et al (2021) Facial expression description and recognition based on fuzzy semantic concepts. Future Gener Comput Syst 114:619–628

    Article  Google Scholar 

  • Liu X, Liu W (2008) The framework of axiomatics fuzzy sets based fuzzy classifiers. J Ind Manag Optim 4(3):581–609

    Article  MathSciNet  Google Scholar 

  • Liu X, Pedrycz W (2009) Axiomatic fuzzy set theory and its applications, vol 244. Springer

    Google Scholar 

  • Liu X, Chai T, Wang W et al (2007) Approaches to the representations and logic operations of fuzzy concepts in the framework of axiomatic fuzzy set theory I. Inf Sci 177(4):1007–1026

    Article  MathSciNet  Google Scholar 

  • Liu X, Feng X, Pedrycz W (2013) Extraction of fuzzy rules from fuzzy decision trees: an axiomatic fuzzy sets (AFS) approach. Data Knowl Eng 84:1–25

    Article  Google Scholar 

  • Liu X, Jia W, Liu W et al (2019) Afsse: an interpretable classifier with axiomatic fuzzy set and semantic entropy. IEEE Trans Fuzzy Syst PP(99):1

    Article  Google Scholar 

  • Loh WY (2011) Classification and regression trees. Wiley Interdiscip Rev Data Min Knowl Discov 1(1):14–23

    Article  Google Scholar 

  • Majumdar S, Laha AK (2020) Clustering and classification of time series using topological data analysis with applications to finance. Expert Syst Appl 162:113868

    Article  Google Scholar 

  • Mucherino A, Papajorgji PJ, Pardalos PM et al (2009) K-nearest neighbor classification. In: Data mining in agriculture, pp 83–106

  • Murtagh F (1991) Multilayer perceptrons for classification and regression. Neurocomputing 2(5–6):183–197

    Article  MathSciNet  Google Scholar 

  • Pedrycz W (2018) Granular computing: analysis and design of intelligent systems. CRC Press

    Book  Google Scholar 

  • Pedrycz W, Al-Hmouz R, Balamash AS et al (2015a) Hierarchical granular clustering: an emergence of information granules of higher type and higher order. IEEE Trans Fuzzy Syst 23(6):2270–2283

    Article  Google Scholar 

  • Pedrycz W, Succi G, Sillitti A et al (2015b) Data description: a general framework of information granules. Knowl-Based Syst 80:98–108

    Article  Google Scholar 

  • Popescu MC, Balas VE, Perescu-Popescu L et al (2009) Multilayer perceptron and neural networks. WSEAS Trans Circuits Syst 8(7):579–588

    Google Scholar 

  • Qian W, Xu F, Qian J et al (2023) Multi-label feature selection based on rough granular-ball and label distribution. Inf Sci 650:119698

    Article  Google Scholar 

  • Qin J, Ma X, Liang Y (2023a) Building a consensus for the best-worst method in group decision-making with an optimal allocation of information granularity. Inf Sci 619:630–653

    Article  Google Scholar 

  • Qin J, Martínez L, Pedrycz W et al (2023b) An overview of granular computing in decision-making: extensions, applications, and challenges. Inf Fusion 2023:101833

    Article  Google Scholar 

  • Rigatti SJ (2017) Random forest. J Insur Med 47(1):31–39

    Article  Google Scholar 

  • Scholkopf B, Sung KK, Burges CJ et al (1997) Comparing support vector machines with gaussian kernels to radial basis function classifiers. IEEE Trans Signal Process 45(11):2758–2765

    Article  Google Scholar 

  • Schulz E, Speekenbrink M, Krause A (2018) A tutorial on gaussian process regression: modelling, exploring, and exploiting functions. J Math Psychol 85:1–16

    Article  MathSciNet  Google Scholar 

  • Shen Y, Pedrycz W, Wang X (2018) Clustering homogeneous granular data: formation and evaluation. IEEE Trans Cybern 49(4):1391–1402

    Article  Google Scholar 

  • Suthaharan S, Suthaharan S (2016) Support vector machine. In: Machine learning models and algorithms for big data classification: thinking with examples for effective learning. Springer, New York, pp 207–235

  • Vert JP, Tsuda K, Schölkopf B (2004) A primer on kernel methods. Kernel Methods Comput Biol 47:35–70

    Google Scholar 

  • Wang AX, Chukova SS, Nguyen BP (2023a) Ensemble k-nearest neighbors based on centroid displacement. Inf Sci 629:313–323

    Article  Google Scholar 

  • Wang X, Yang J, Lu W (2023b) Bearing fault diagnosis algorithm based on granular computing. Granul Comput 8(2):333–344

    Article  Google Scholar 

  • **aodong L (1998) Fuzzy sets and systems based on AFS/structure, EI algebra and EII algebra. Fuzzy Sets Syst 95(2):179–188

    Article  MathSciNet  Google Scholar 

  • **ng W, Bei Y (2019) Medical health big data classification based on KNN classification algorithm. IEEE Access 8:28808–28819

    Article  Google Scholar 

  • Xu L, Zhou X, Ren Y et al (2019) A traffic classification method based on packet transport layer payload by ensemble learning. In: 2019 IEEE Symposium on Computers and Communications (ISCC). IEEE, pp 1–6

  • Yan R, Liu X, Cao J (2011) A parsimony fuzzy rule-based classifier using axiomatic fuzzy set theory and support vector machines. Inf Sci 181(23):5180–5193

    Article  Google Scholar 

  • Yao JT, Vasilakos AV, Pedrycz W (2013) Granular computing: perspectives and challenges. IEEE Trans Cybern 43(6):1977–1989

    Article  Google Scholar 

  • Yin R, Lu W, Yang J (2024) A hypersphere information granule-based fuzzy classifier embedded with fuzzy cognitive maps for classification of imbalanced data. IEEE Trans Emerg Top Comput Intell 8:175–190

    Article  Google Scholar 

  • Ying C, Qi-Guang M, Jia-Chen L et al (2013) Advance and prospects of adaboost algorithm. Acta Autom Sin 39(6):745–758

    Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  Google Scholar 

  • Zhong H, Wang Y, Tu C et al (2020) Iteratively questioning and answering for interpretable legal judgment prediction. In: Proceedings of the AAAI Conference on Artificial Intelligence, pp 1250–1257

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 62073056 and 61876029; in part by the Applied Basic Research Program Project of Liaoning Province under Grant 2023JH2/101300207 and in part by the Key Field Innovation Team Project of Dalian under Grant 2021RT14.

Author information

Authors and Affiliations

  1. School of Control Science and Engineering, Dalian University of Technology, No. 2 Lingong Road, Dalian, 116023, Liaoning, China

    Han-Shen Wang & Wei Lu

  2. State Grid Dalian Electric Power Company, Dalian, 116001, Liaoning, China

    Han-Shen Wang

Authors
  1. Han-Shen Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Han-Shen Wang completed the experiments and wrote the main manuscript. Wei Lu provided some main ideas and methodology. All authors reviewed the manuscript.

Corresponding author

Correspondence to Wei Lu.

Ethics declarations

Conflict of interest

The authors declare they have no conflict of interest.

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

Wang, HS., Lu, W. An interpretable hypersphere information granule-based classifier for numeric data using axiomatic fuzzy set. Granul. Comput. 9, 66 (2024). https://doi.org/10.1007/s41066-024-00488-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s41066-024-00488-0

Keywords

Search

Navigation