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Fuzzy Entropy Used for Predictive Analytics

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Fuzzy Logic in Its 50th Year

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 341))

Abstract

Process interruptions in (very) large production systems are difficult to deal with. Modern processes are highly automated; data is collected with sensor technology that forms a big data context and offers challenges to identify coming failures from the very large sets of data. The sensors collect huge amounts of data but the failure events are few and infrequent and hard to find (and even harder to predict). In this article, our goal is to develop models for predictive maintenance in a big data environment. The purpose of feature selection in the context of predictive maintenance is to identify a small set of process diagnostics that are sufficient to predict future failures. We apply interval-valued fuzzy sets and various entropy measures defined on them to perform feature selection on process diagnostics. We show how these models can be utilized as the basis of decision support systems in process industries to aid predictive maintenance.

A preliminary version of this chapter was presented at the 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2015).

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References

  1. Beath, C., Becerra-Fernandez, I., Ross, J., Short, J.: Finding value in the information explosion. MIT Sloan Manage. Rev. 53(4), 18 (2012)

    Google Scholar 

  2. Bolón-Canedo, V., Sánchez-Maroño, N., Alonso-Betanzos, A.: Recent advances and emerging challenges of feature selection in the context of big data. Knowl. Based Syst. 86, 33–45 (2015)

    Article  Google Scholar 

  3. Burillo, P., Bustince, H.: Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst. 78(3), 305–316 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  4. Carlsson, C., Fullér, R.: Fuzzy Reasoning in Decision Making and Optimization, vol. 82. Springer Science & Business Media (2002)

    Google Scholar 

  5. Carlsson, C., Heikkilä, M., Mezei, J.: Possibilistic Bayes modelling for predictive analytics. In: 2014 IEEE 15th International Symposium on Computational Intelligence and Informatics (CINTI), pp. 15–20. IEEE (2014)

    Google Scholar 

  6. Chen, H., Chiang, R.H., Storey, V.C.: Business intelligence and analytics: from big data to big impact. MIS Q. 36(4), 1165–1188 (2012)

    Google Scholar 

  7. Dash, M., Liu, H.: Feature selection for classification. Intel. Data Anal. 1(3), 131–156 (1997)

    Article  Google Scholar 

  8. Davenport, T.H., Harris, J.G.: Competing on Analytics: The New Science of Winning. Harvard Business Press (2007)

    Google Scholar 

  9. De Luca, A., Termini, S.: A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Inf. Control 20(4), 301–312 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  10. De Mántaras, R.L.: A distance-based attribute selection measure for decision tree induction. Mach. Learn. 6(1), 81–92 (1991)

    Article  Google Scholar 

  11. Demirkan, H., Delen, D.: Leveraging the capabilities of service-oriented decision support systems: putting analytics and big data in cloud. Dec. Supp. Syst. 55(1), 412–421 (2013)

    Article  Google Scholar 

  12. Diamantoulakis, P.D., Kapinas, V.M., Karagiannidis, G.K.: Big data analytics for dynamic energy management in smart grids. Big Data Res. 2(3), 94–101 (2015)

    Article  Google Scholar 

  13. Gandomi, A., Haider, M.: Beyond the hype: big data concepts, methods, and analytics. Int. J. Inf. Manage. 35(2), 137–144 (2015)

    Article  Google Scholar 

  14. Gass, S.I., Harris, C.M. (eds.): Encyclopedia of Operations Research and Management Science. Kluwer Academic Publishers, Dordrecht (1996)

    Google Scholar 

  15. Gil-Aluja, J.: Fuzzy Sets in the Management of Uncertainty. Springer Science & Business Media (2004)

    Google Scholar 

  16. Gorzałczany, M.B.: A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 21(1), 1–17 (1987)

    Google Scholar 

  17. Guyon, I., Elisseeff, A.: An introduction to variable and feature selection. J. Mach. Learn. Res. 3, 1157–1182 (2003)

    MATH  Google Scholar 

  18. Hall, M.A.: Correlation-based feature selection for machine learning. Ph.D. thesis, The University of Waikato (1999)

    Google Scholar 

  19. Hitzler, P., Janowicz, K.: Linked data, big data, and the 4th paradigm. Seman. Web 4(3), 233–235 (2013)

    Google Scholar 

  20. Janke, A.T., Overbeek, D.L., Kocher, K.E., Levy, P.D.: Exploring the potential of predictive analytics and big data in emergency care. Ann. Emerg. Med. (2015)

    Google Scholar 

  21. Jiang, Y., Tang, Y., Liu, H., Chen, Z.: Entropy on intuitionistic fuzzy soft sets and on interval-valued fuzzy soft sets. Inf. Sci. 240, 95–114 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  22. Knopfmacher, J.: On measures of fuzziness. J. Math. Anal. Appl. 49(3), 529–534 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  23. Kosko, B.: Fuzzy entropy and conditioning. Inf. Sci. 40(2), 165–174 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  24. Kwak, N., Choi, C.-H.: Input feature selection for classification problems. IEEE Trans. Neural Netw. 13(1), 143–159 (2002)

    Article  Google Scholar 

  25. Lee, H.-M., Chen, C.-M., Chen, J.-M., Jou, Y.-L.: An efficient fuzzy classifier with feature selection based on fuzzy entropy. IEEE Trans. Syst. Man Cybern. Part B Cybern. 31(3), 426–432 (2001)

    Article  Google Scholar 

  26. Lee, S.-H., Kim, S., Kim, J.-M., Choi, C., Kim, J., Lee, S., Oh, Y.: Extraction of induction motor fault characteristics in frequency domain and fuzzy entropy. In: 2005 IEEE International Conference on Electric Machines and Drives, pp. 35–40. IEEE (2005)

    Google Scholar 

  27. Li, P., Liu, B.: Entropy of credibility distributions for fuzzy variables. IEEE Trans. Fuzzy Syst. 1(16), 123–129 (2008)

    Google Scholar 

  28. Li, J., Deng, G., Li, H., Zeng, W.: The relationship between similarity measure and entropy of intuitionistic fuzzy sets. Inf. Sci. 188, 314–321 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  29. Liu, X.: Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets Syst. 52(3), 305–318 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  30. Liu, B.: Uncertainty Theory. Springer, Berlin (2007)

    Book  MATH  Google Scholar 

  31. Liu, H., Yu, L.: Toward integrating feature selection algorithms for classification and clustering. IEEE Knowl. Data Eng. 17(4), 491–502 (2005)

    Article  Google Scholar 

  32. McAfee, A., Brynjolfsson, E.: Big data: the management revolution. Harvard Bus. Rev. 90(10), 60–68 (2012)

    Google Scholar 

  33. Mezei, J., Morente-Molinera, J.A., Carlsson, C.: Feature selection with fuzzy entropy to find similar cases. In: Advance Trends in Soft Computing, pp. 383–390. Springer, Berlin (2014)

    Google Scholar 

  34. Morabito, V.: Big data driven business models. In: Big Data and Analytics, pp. 65–80. Springer, Berlin (2015)

    Google Scholar 

  35. Muir, B.M., Moray, N.: Trust in automation. Part ii. Experimental studies of trust and human intervention in a process control simulation. Ergonomics 39(3), 429–460 (1996)

    Article  Google Scholar 

  36. Nieto-Santisteban, M.A., Szalay, A.S., Thakar, A.R., O’Mullane, W.J., Gray, J., Annis, J.: When database systems meet the grid. arXiv preprint cs/0502018 (2005)

    Google Scholar 

  37. Papermaking—Parts 1–3. Paperi ja Puu Oy, Jyväskylä (2007)

    Google Scholar 

  38. Parthalain, N., Jensen, R., Shen, Q.: Fuzzy entropy-assisted fuzzy-rough feature selection. In: 2006 IEEE International Conference on Fuzzy Systems, pp. 423–430. IEEE (2006)

    Google Scholar 

  39. Qin, S.J.: Process data analytics in the era of big data. AIChE J. 60(9), 3092–3100 (2014)

    Article  Google Scholar 

  40. R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2014)

    Google Scholar 

  41. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(3), 379–423 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  42. Shie, J.-D., Chen, S.-M.: Feature subset selection based on fuzzy entropy measures for handling classification problems. Appl. Intell. 28(1), 69–82 (2008)

    Article  Google Scholar 

  43. Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Set. Syst. 118(3), 467–477 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  44. Tao, W.-B., Tian, J.-W., Liu, J.: Image segmentation by three-level thresholding based on maximum fuzzy entropy and genetic algorithm. Patt. Rec. Lett. 24(16), 3069–3078 (2003)

    Article  Google Scholar 

  45. Wu, D., Mendel, J.M.: Uncertainty measures for interval type-2 fuzzy sets. Inf. Sci. 177(23), 5378–5393 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  46. Wu, X., Gu, H., Hu, X., Dong, Y.: Application of the fuzzy entropy weight in risk assessment of the engineering project. In: Fifth International Conference on Information Assurance and Security, vol. 1, pp. 145–148. IEEE (2009)

    Google Scholar 

  47. Xu, Z., Xia, M.: Hesitant fuzzy entropy and cross-entropy and their use in multiattribute decision-making. Int. J. Intell. Syst. 27(9), 799–822 (2012)

    Article  Google Scholar 

  48. Yager, R.R.: A procedure for ordering fuzzy subsets of the unit interval. Inf. Sci. 24(2), 143–161 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  49. Ye, J.: Fault diagnosis of turbine based on fuzzy cross entropy of vague sets. Expert Syst. Appl. 36(4), 8103–8106 (2009)

    Article  Google Scholar 

  50. Zadeh, L.A.: Fuzzy sets. Inform. Cont. 8(3), 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  51. Zeng, W., Li, H.: Relationship between similarity measure and entropy of interval valued fuzzy sets. Fuzzy Sets Syst. 157(11), 1477–1484 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  52. Zhai, Y., Ong, Y.-S., Tsang, I.W.: The emerging “big dimensionality”. IEEE Comput. Intell. Mag. 9(3), 14–26 (2014)

    Article  Google Scholar 

  53. Zhang, Q.-S., Jiang, S.-Y.: A note on information entropy measures for vague sets and its applications. Inf. Sci. 178(21), 4184–4191 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  54. Zikopoulos, P., Eaton, C.: Understanding big data: analytics for enterprise class hadoop and streaming data. McGraw-Hill Osborne Media, New York (2011)

    Google Scholar 

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Acknowledgment

This research has been funded through the TEKES strategic research project Data to Intelligence [D2I], project number: 340/12.

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Correspondence to Christer Carlsson .

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Carlsson, C., Heikkilä, M., Mezei, J. (2016). Fuzzy Entropy Used for Predictive Analytics. In: Kahraman, C., Kaymak, U., Yazici, A. (eds) Fuzzy Logic in Its 50th Year. Studies in Fuzziness and Soft Computing, vol 341. Springer, Cham. https://doi.org/10.1007/978-3-319-31093-0_9

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  • DOI: https://doi.org/10.1007/978-3-319-31093-0_9

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