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Curvature-Based Sparse Rule Base Generation for Fuzzy Interpolation Using Menger Curvature

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Advances in Computational Intelligence Systems (UKCI 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1043))

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Abstract

Fuzzy interpolation improves the applicability of fuzzy inference by allowing the utilisation of sparse rule bases. Curvature-based rule base generation approach has been recently proposed to support fuzzy interpolation. Despite the ability to directly generating sparse rule bases from data, the approach often suffers from the high dimensionality of complex inference problems. In this work, a different curvature calculation approach, i.e., the Menger approach, is employed to the curvature-based rule base generation approach in an effort to address the limitation. The experimental results confirm better efficiency and efficacy of the proposed method in generating rule bases on high-dimensional datasets.

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References

  1. Kóczy, L.T., Hirota, K.: Approximate reasoning by linear rule interpolation and general approximation. Int. J. Appox. Reason. 9(3), 197–225 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  2. Huang, Z., Shen, Q.: Fuzzy interpolative reasoning via scale and move transformations. IEEE Trans. Fuzzy Syst. 14(2), 340–359 (2006)

    Article  Google Scholar 

  3. Huang, Z., Shen, Q.: Fuzzy interpolation and extrapolation: a practical approach. IEEE Trans. Fuzzy Syst. 16(1), 13–28 (2008)

    Article  Google Scholar 

  4. Shen, Q., Yang, L.: Generalisation of scale and move transformation-based fuzzy interpolation. J. Adv. Comput. Intell. Intell. Inform. 15(3), 288–298 (2011)

    Article  Google Scholar 

  5. Li, J., Qu, Y., Shum, H.P.H., Yang, L.: TSK inference with sparse rule bases. In: Proceedings of UK Workshop on Computational Intelligence, pp. 107–123 (2016)

    Google Scholar 

  6. Yang, L., Shen, Q.: Adaptive fuzzy interpolation. IEEE Trans. Fuzzy Syst. 19(6), 1107–1126 (2011)

    Article  Google Scholar 

  7. Yang, L., Shen, Q.: Closed form fuzzy interpolation. Fuzzy Sets Syst. 225, 1–22 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Yang, L., Chao, F., Shen, Q.: Generalized adaptive fuzzy rule interpolation. IEEE Trans. Fuzzy Syst. 25(4), 839–853 (2016)

    Article  Google Scholar 

  9. Zuo, Z., Li, J., Anderson, P., Yang, L., Naik, N.: Grooming detection using fuzzy-rough feature selection and text classification. In: Proceedings of IEEE International Conference on Fuzzy Systems, pp. 1–8 (2018)

    Google Scholar 

  10. Elisa, N., Li, J., Zuo, Z., Yang, L.: Dendritic cell algorithm with fuzzy inference system for input signal generation. In: Proceedings of UK Workshop on Computational Intelligence, pp. 203–214 (2018)

    Google Scholar 

  11. Zuo, Z., Li, J., Wei, B., Yang, L., Chao, F., Naik, N.: Adaptive activation function generation for artificial neural networks through fuzzy inference with application in grooming text categorisation. In: Proceedings of IEEE International Conference on Fuzzy System (2019)

    Google Scholar 

  12. Li, J., Yang, L., Shum, H.P.H., Sexton, G., Tan, Y.: Intelligent home heating controller using fuzzy rule interpolation. In: Proceedings of UK Workshop on Computational Intelligence (2015)

    Google Scholar 

  13. Li, J., Yang, L., Fu, X., Chao, F., Qu, Y.: Dynamic QoS solution for enterprise networks using TSK fuzzy interpolation. In: Proceedings of IEEE International Conference on Fuzzy Systems, pp. 1–6 (2017)

    Google Scholar 

  14. Yin, K., Xiang, K., Pang, M., Chen, J., Anderson, P., Yang, L.: Personalised control of robotic ankle exoskeleton through experience-based adaptive fuzzy inference. IEEE Access 7, 72221–72233 (2019)

    Article  Google Scholar 

  15. Yang, L., Li, J., Chao, F., Hackney, P., Flanagan, M.: Job shop planning and scheduling for manufacturers with manual operations. Expert Syst. e12315 (2018)

    Google Scholar 

  16. Koczy, L.T., Hirota, K.: Size reduction by interpolation in fuzzy rule bases. IEEE Trans. Syst., Man, Cybern. 27(1), 14–25 (1997)

    Article  Google Scholar 

  17. Li, J., Shum, H.P.H., Fu, X., Sexton, G., Yang, L.: Experience-based rule base generation and adaptation for fuzzy interpolation. In: Proceedings of IEEE International Conference on Fuzzy Systems, pp, 102–109 (2016)

    Google Scholar 

  18. Tao, C.-W.: A reduction approach for fuzzy rule bases of fuzzy controllers. IEEE Trans. Syst., Man, Cybern. B. Cybern. 32(5), 668–675 (2002)

    Article  Google Scholar 

  19. Tan, Y., Shum, H.P.H., Chao, F., Vijayakumar, V., Yang, L.: Curvature-based sparse rule base generation for fuzzy rule interpolation. J. Intell. Fuzzy Syst. 36(5), 4201–4214 (2019)

    Article  Google Scholar 

  20. Tan, Y., Li, J., Wonders, M., Chao, F., Shum, H.P.H., Yang, L.: Towards sparse rule base generation for fuzzy rule interpolation. In: Proceedings of IEEE International Conference on Fuzzy Systems, pp. 110–117 (2016)

    Google Scholar 

  21. Peckham, S.D.: Profile, plan and streamline curvature: a simple derivation and applications. In: Proceedings of Geomorphometry, vol. 4, pp. 27–30 (2011)

    Google Scholar 

  22. Li, J., Yang, L., Qu, Y., Sexton, G.: An extended Takagi-Sugeno-Kang inference system (TSK+) with fuzzy interpolation and its rule base generation. Soft Comput. 22(10), 3155–3170 (2018)

    Article  Google Scholar 

  23. Léger, J.-C.: Menger curvature and rectifiability. Ann. Math. 149, 831–869 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  24. Jensen, R., Shen, Q.: New approaches to fuzzy-rough feature selection. IEEE Trans. Fuzzy Syst. 17(4), 824–838 (2008)

    Article  Google Scholar 

  25. Tharwat, A., Gaber, T., Ibrahim, A., Hassanien, A.E.: Linear discriminant analysis: a detailed tutorial. AI Commun. 30(2), 169–190 (2017)

    Article  MathSciNet  Google Scholar 

  26. Suckling, J., Parker, J., Dance, D., Astley, S., Hutt, I., Boggis, C., Ricketts, I.: Mammographic Image Analysis Society (MIAS) database v1.21 (2015). https://www.repository.cam.ac.uk/handle/1810/250394/

  27. Boyd, N.F., Byng, J.W., Jong, R.A., Fishell, E.K., Little, L.E., Miller, A.B., Lockwood, G.A., Tritchler, D.L., Yaffe, M.J.: Quantitative classification of mammographic densities and breast cancer risk: results from the Canadian National Breast Screening Study. J. Natl. Cancer Inst. 87(9), 670–675 (1995)

    Article  Google Scholar 

  28. Aha, D.W., Kibler, D., Albert, M.K.: Instance-based learning algorithms. Mach. Learn. 6(1), 37–66 (1991)

    Google Scholar 

  29. Qu, Y., Shang, C., Parthaláin, N.M., Wu, W., Shen, Q.: Multi-functional nearest-neighbour classification. Soft Comput. 22(8), 2717–2730 (2018)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Comptuer and Informaiton Sciences, Northumbria University, Newcastle upon Tyne, NE1 8ST, UK

    Zheming Zuo & Longzhi Yang

  2. School of Computing & Digital Technologies, Teesside University, Middlesbrough, UK

    Jie Li

Authors
  1. Zheming Zuo
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  2. Jie Li
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  3. Longzhi Yang
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Corresponding author

Correspondence to Longzhi Yang .

Editor information

Editors and Affiliations

  1. School of Computing, University of Portsmouth, Portsmouth, UK

    Zhaojie Ju

  2. Department of Computer and Information Sciences, Northumbria University, Newcastle upon Tyne, UK

    Longzhi Yang

  3. Bristol Robotics Laboratory, University of the West of England, Bristol, UK

    Chenguang Yang

  4. School of Computing, University of Portsmouth, Portsmouth, Hampshire, UK

    Alexander Gegov

  5. School of Computing, University of Portsmouth, Portsmouth, UK

    Dalin Zhou

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Zuo, Z., Li, J., Yang, L. (2020). Curvature-Based Sparse Rule Base Generation for Fuzzy Interpolation Using Menger Curvature. In: Ju, Z., Yang, L., Yang, C., Gegov, A., Zhou, D. (eds) Advances in Computational Intelligence Systems. UKCI 2019. Advances in Intelligent Systems and Computing, vol 1043. Springer, Cham. https://doi.org/10.1007/978-3-030-29933-0_5

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