Bayesian Logistic Regression using Vectorial Centroid for Interval Type-2 Fuzzy Sets

Ku Muhammad Naim Ku Khalif, Alexander Gegov

2015

Abstract

It is necessary to represent the probabilities of fuzzy events based on a Bayesian knowledge. Inspired by such real applications, in this research study, the theoretical foundations of Vectorial Centroid of interval type-2 fuzzy sets with Bayesian logistic regression is introduced. This includes official models, elementary operations, basic properties and advanced application. The Vectorial Centroid method for interval type-2 fuzzy set takes a broad view by exampled labelled by a classical Vectorial Centroid defuzzification method for type-1 fuzzy sets. Rather than using type-1 fuzzy sets for implementing fuzzy events, type-2 fuzzy sets are recommended based on the involvement of uncertainty quantity. It also highlights the incorporation of fuzzy sets with Bayesian logistic regression allows the use of fuzzy attributes by considering the need of human intuition in data analysis. It is worth adding here that this proposed methodology then applied for BUPA liver-disorder dataset and validated theoretically and empirically.

References

  1. Carlsson, C., Fuller, R. 2001. On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems, vol. 122.
  2. Chen, C.C.M., Schwender, H., Keith, J., Nunkesser, R., Mengersen, K., Macrossan, P. 2011. Method of identifying SNP interactions: A review on variations of logic regression, random forest and Bayesian logistic regression, IEEE/ ACM Transactions on Computational Biology and Bioinformatics, vol. 8. a Cheng, C.H. 1998. A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems, vol. 95.
  3. Choy, S.L. 2013. Priors: Silent or active partners of Bayesian inference?, Case Studies in Bayesian Statistical Modelling and Analysis, John Wiley & Sons Ltd, Sussex.
  4. Deng, H. 2013. Comparing and ranking fuzzy numbers using ideal solutions, Applied Mathematics Modelling, vol. 38.
  5. Forsyth, R.S. 2015. Liver disorder data set, UCI Machine Learning Repository: Internet Source: https://archive.ics.uci.edu/ml/datasets/Liver+Disorders [Feb. 1, 2015].
  6. Gong, Y., Hu, N., Zhang, J., Liu. G., Deng. J. 2015. Multiattribute group decision making method based on geometric Bonferroni mean operator of trapezoidal interval type-2 fuzzy numbers, Computer and Industrial Engineering, vol. 81.
  7. Hullermeier, E. 2011. Fuzzy sets in machine learning and data mining, Applied Soft Computing, vol. 11.
  8. Jeong, D., Kang, D., Won, S. 2010. Feature selection for steel defects classification, International Conference on Control, Automation and Systems.
  9. Joseph. 2015. Bayesian inference for logistic regression parameters. Internet Source: http://www.medicine. mcgill.ca/epidemiology/joseph/courses/EPIB-621/ bayeslogit.pdf [March, 15, 2015].
  10. Karnik, N.N., Mendel, J.M. 2001. Centroid of type-2 fuzzy set, Information Sciences, vol. 132.
  11. Klir, G., Yuan, B. 1995. Fuzzy sets and fuzzy logic: Theory and applications, Prentice Hall, Upper Saddle River.
  12. Ku Khalif, K.M.N., Gegov, A. 2015. Generalised fuzzy Bayesian network with adaptive Vectorial Centroid, 16th World Congress of the International Fuzzy Systems Association (IFSA) and 9th Conference of European Society for Fuzzy Logic and Technology (EUSFLAT).
  13. Lalkhen, A.G., McCluskey, A. 2015. Clinical test sensitivity and specificity, Internet Source: http://ceaccp.oxfordjournals.org/content/8/6/221.full [March, 16, 2015].
  14. Lee, L.W., Chen, S.M. 2008. Fuzzy multiple attributes group decision-making based on the extension of TOPSIS method and interval type-2 fuzzy sets, 7th IEEE International Conference on Machine Learning and Cybernatics.
  15. Liu. F. 2008. An efficient centroid type-reduction strategy for general type-2 fuzzy logic system, Information Sciences, vol. 178.
  16. Mendel, J.M. 2001. Uncertain rule-based fuzzy logic systems: Introduction and new directions, PrenticeHall, Upper Saddle River, New Jersey.
  17. Mendel, J.M., John, R.I., Liu, F.L. 2006. Interval type-2 fuzzy logical systems made simple, IEEE Transactions on Fuzzy Systems, vol. 14.
  18. Mendel, J.M., Wu, H.W. 2006. Type-2 fuzzistic for symmetric interval type-2 fuzzy sets: Part 1, forward problems, IEEE Transactions on Fuzzy Systems, vol. 14.
  19. Mogharreban, N., Dilalla, L.F. 2006. Comparison of defuzzification techniques for analysis of non-interval data, Fuzzy Information Processing Society.
  20. Tang, Y., Pan, H., Xu, Y. 2002. Fuzzy naïve Bayes classifier based on fuzzy clustering, Systems, Man and Cybernatics, IEEE International Conference, vol. 5.
  21. Wagner, C., Hagras, H. 2010. Uncertainty and type-2 fuzzy sets systems, IEEE UK Workshop on Computational Intelligent (UKCI).
  22. Wallsten, T.S., Budescu, D.V. 1995. A review of human linguistic probability processing general principles and empirical evidences, The Knowledge Engineering Review, vol.10 (a).
  23. Yager, R.R., Filev, D.P. 1994. Essential of fuzzy modelling and control, Wiley, New York.
  24. Zadeh, L.A. 1965. Fuzzy sets, Information and Control, vol. 8.
  25. Zadeh, L.A., 1975. The concept of a linguistic variable and its application to approximate reasoning, Information Sciences, vol. 8.
  26. Zimmermann, H.J. 2000. An application - oriented view of modelling uncertainty, European Journal of Operational Research, vol 122.
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Paper Citation


in Harvard Style

Ku Khalif K. and Gegov A. (2015). Bayesian Logistic Regression using Vectorial Centroid for Interval Type-2 Fuzzy Sets . In Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 2: FCTA, (ECTA 2015) ISBN 978-989-758-157-1, pages 69-79. DOI: 10.5220/0005614400690079


in Bibtex Style

@conference{fcta15,
author={Ku Muhammad Naim Ku Khalif and Alexander Gegov},
title={Bayesian Logistic Regression using Vectorial Centroid for Interval Type-2 Fuzzy Sets},
booktitle={Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 2: FCTA, (ECTA 2015)},
year={2015},
pages={69-79},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005614400690079},
isbn={978-989-758-157-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 2: FCTA, (ECTA 2015)
TI - Bayesian Logistic Regression using Vectorial Centroid for Interval Type-2 Fuzzy Sets
SN - 978-989-758-157-1
AU - Ku Khalif K.
AU - Gegov A.
PY - 2015
SP - 69
EP - 79
DO - 10.5220/0005614400690079