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An Alternative to Power Measure for Fuzzy Rule-Based Classification Systems

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Intelligent Systems (BRACIS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12320))

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Abstract

An effective way to deal with classification problems, among other approaches, is using Fuzzy Rule-Based Classification Systems (FRBCSs). These classification systems are mainly composed of two modules, the Knowledge Base (KB) and the Fuzzy Reasoning Method (FRM). The KB is responsible for storing information related to the problem, while the FRM performs the classification of new examples based on the KB. A key point in the FRM is how the information given by the triggered fuzzy rules is aggregated. Several FRMs have been proposed in the literature employing generalizations of the Choquet Integral as the aggregation function. The usage of this function to perform the aggregation is efficient because it uses fuzzy measures to model the interrelationships between the data. Indeed, the performance of the classification system is strongly related to the underlying fuzzy measure. However, many of those generalizations have used fuzzy measures that do not properly model the interaction between the data. In this context, we intend to enhance the way how the relationships between the rules are modeled in the FRM of an FRBCS. In order to accomplish that, we propose the use of a well known fuzzy measure, the Sugeno lambda, as an alternative to the Power Measure, which is widely used in many generalizations of the Choquet Integral. The experimental evaluation shows statistical equivalent results comparing our method with the state-of-the-art fuzzy classifier.

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References

  1. Abe, S., Thawonmas, R.: A fuzzy classifier with ellipsoidal regions. IEEE Trans. Fuzzy Syst. 5(3), 358–368 (1997)

    Article  Google Scholar 

  2. Alcala-Fdez, J., Alcala, R., Herrera, F.: A fuzzy association rule-based classification model for high-dimensional problems with genetic rule selection and lateral tuning. IEEE Trans. Fuzzy Syst. 19(5), 857–872 (2011)

    Article  Google Scholar 

  3. Alcalá-Fdez, J., et al.: KEEL: a software tool to assess evolutionary algorithms for data mining problems. Soft Comput. 13(3), 307–318 (2009)

    Article  Google Scholar 

  4. Bárdossy, A., Samaniego, L.: Fuzzy rule-based classification of remotely sensed imagery. IEEE Trans. Geosci. Remote Sens. 40(2), 362–374 (2002)

    Article  Google Scholar 

  5. Barrenechea, E., Bustince, H., Fernandez, J., Paternain, D., Sanz, J.A.: Using the choquet integral in the fuzzy reasoning method of fuzzy rule-based classification systems. Axioms 2(2), 208–223 (2013)

    Article  Google Scholar 

  6. Beliakov, G., Pradera, A., Calvo, T., et al.: Aggregation Functions: A Guide for Practitioners, vol. 221. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73721-6

  7. Bicego, M., Grosso, E., Otranto, E.: A hidden Markov model approach to classify and predict the sign of financial local trends. In: da Vitoria Lobo, N., et al. (eds.) SSPR /SPR 2008. LNCS, vol. 5342, pp. 852–861. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89689-0_89

    Chapter  Google Scholar 

  8. Borneman, J.: Race, ethnicity, species, breed: Totemism and horse-breed classification in America. Comparative Stud. Soc. History 30(1), 25–51 (1988)

    Article  Google Scholar 

  9. Cao, Y.: Aggregating multiple classification results using choquet integral for financial distress early warning. Expert Syst. Appl. 39(2), 1830–1836 (2012)

    Article  Google Scholar 

  10. Chi, Z., Yan, H., Pham, T.: Fuzzy algorithms: with applications to image processing and pattern recognition, vol. 10. World Scientific (1996)

    Google Scholar 

  11. Choquet, G.: 54, “theory of capacities”. Ann. Inst. Fourier 5(131), 295 (1953)

    MATH  Google Scholar 

  12. Cordón, O., Del Jesus, M.J., Herrera, F.: A proposal on reasoning methods in fuzzy rule-based classification systems. Int. J. Approximate Reason. 20(1), 21–45 (1999)

    Article  Google Scholar 

  13. Dean, J., Ghemawat, S.: Mapreduce: simplified data processing on large clusters. Commun. ACM 51(1), 107–113 (2008)

    Article  Google Scholar 

  14. Deshpande, A., Guestrin, C., Madden, S.R., Hellerstein, J.M., Hong, W.: Model-driven data acquisition in sensor networks. In: Proceedings of the Thirtieth International Conference on Very Large Data Bases, vol. 30, pp. 588–599 (2004)

    Google Scholar 

  15. Dimuro, G.P., et al.: The state-of-art of the generalizations of the choquet integral: from aggregation and pre-aggregation to ordered directionally monotone functions. Inf. Fusion 57, 27–43 (2020)

    Article  Google Scholar 

  16. Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. Wiley, Hoboken (2012)

    Google Scholar 

  17. Elkano, M., Galar, M., Sanz, J., Bustince, H.: CHI-BD: a fuzzy rule-based classification system for big data classification problems. Fuzzy Sets Syst. 348, 75–101 (2018)

    Article  MathSciNet  Google Scholar 

  18. Flanagan, M.T.: Michael Thomas Flanagan’s Java scientific library (2007)

    Google Scholar 

  19. Giannoglou, V.G., Stavrakoudis, D.G., Theocharis, J.B., Petridis, V.: Genetic fuzzy rule-based classification systems for tissue characterization of intravascular ultrasound images. In: 2012 IEEE International Conference on Fuzzy Systems, pp. 1–8. IEEE (2012)

    Google Scholar 

  20. González, A., Pérez, R., Romero-Záliz, R.: Reasoning methods in fuzzy rule-based classification systems for big data problems. In: IoTBDS (2019)

    Google Scholar 

  21. Grabisch, M.: A new algorithm for identifying fuzzy measures and its application to pattern recognition. In: Proceedings of 1995 IEEE International Conference on Fuzzy Systems, vol. 1, pp. 145–150. IEEE (1995)

    Google Scholar 

  22. Han, J., Pei, J., Kamber, M.: Data Mining: Concepts and Techniques. Elsevier (2011)

    Google Scholar 

  23. Holmes, I.J.S., Anderson, J.E.: Glucose test data acquisition and management system (Dec 6 1994), uS Patent 5,371,687

    Google Scholar 

  24. Ishibuchi, H., Nakashima, T., Morisawa, T.: Voting in fuzzy rule-based systems for pattern classification problems. Fuzzy Sets Syst. 103(2), 223–238 (1999)

    Article  Google Scholar 

  25. Ishibuchi, H., Nakashima, T., Nii, M.: Classification and Modeling with Linguistic Information Granules: Advanced Approaches to Linguistic Data Mining. Springer, Heidelberg (2004). https://doi.org/10.1007/b138232

  26. Keller, J.M., Osborn, J.: Training the fuzzy integral. Int. J. Approximate Reason. 15(1), 1–24 (1996)

    Article  Google Scholar 

  27. Kim, S.Y., et al.: Classification of usual interstitial pneumonia in patients with interstitial lung disease: assessment of a machine learning approach using high-dimensional transcriptional data. Lancet Resp. Med. 3(6), 473–482 (2015)

    Article  Google Scholar 

  28. Kuncheva, L.: Fuzzy Classifier Design, vol. 49. Springer, Heidelberg (2000). https://doi.org/10.1007/978-3-7908-1850-5

  29. Leszczyński, K., Penczek, P., Grochulski, W.: Sugeno’s fuzzy measure and fuzzy clustering. Fuzzy Sets Syst. 15(2), 147–158 (1985)

    Article  MathSciNet  Google Scholar 

  30. Lucca, G.: Aggregation and pre-aggregation functions in fuzzy rule-based classification systems (2018)

    Google Scholar 

  31. Lucca, G., et al.: Preaggregation functions: construction and an application. IEEE Trans. Fuzzy Syst. 24(2), 260–272 (2015)

    Article  Google Scholar 

  32. Magadum, C., Bapat, M.: Ranking of students for admission process by using choquet integral. Int. J. Fuzzy Math. Arch. 15(2), 105–113 (2018)

    Google Scholar 

  33. Michie, D., Spiegelhalter, D.J., Taylor, C., et al.: Machine learning. Neural Stat. Classif. 13(1994), 1–298 (1994)

    MATH  Google Scholar 

  34. Murofushi, T., Sugeno, M., Machida, M.: Non-monotonic fuzzy measures and the choquet integral. Fuzzy Sets Syst. 64(1), 73–86 (1994)

    Article  MathSciNet  Google Scholar 

  35. Murofushi, T., Sugeno, M., et al.: Fuzzy measures and fuzzy integrals. Fuzzy measures and integrals: theory and applications, pp. 3–41 (2000)

    Google Scholar 

  36. Nguyen, H.T., Kreinovich, V., Lorkowski, J., Abu, S.: Why Sugeno lambda-Measures. Departmental Technical Reports (CS) (2015)

    Google Scholar 

  37. Provost, F., Fawcett, T.: Data science and its relationship to big data and data-driven decision making. Big Data 1(1), 51–59 (2013)

    Article  Google Scholar 

  38. He, Q., Chen, J.-F., Yuan, X.-Q., Li, J.: Choquet fuzzy integral aggregation based on g-lambda fuzzy measure. In: 2007 International Conference on Wavelet Analysis and Pattern Recognition, vol. 1, pp. 98–102 (2007)

    Google Scholar 

  39. Sanz, J.A., Galar, M., Jurio, A., Brugos, A., Pagola, M., Bustince, H.: Medical diagnosis of cardiovascular diseases using an interval-valued fuzzy rule-based classification system. Appl. Soft Comput. 20, 103–111 (2014)

    Article  Google Scholar 

  40. Sugeno, M.: Theory of fuzzy integrals and its applications. Doctoral thesis, Tokyo Institute of technology (1974)

    Google Scholar 

  41. Uebele, V., Abe, S., Lan, M.S.: A neural-network-based fuzzy classifier. IEEE Trans. Syst. Man Cybern. 25(2), 353–361 (1995)

    Article  Google Scholar 

  42. Verma, N.K.: Estimation of fuzzy measures using covariance matrices in gaussian mixtures. Appl. Comput. Intell. Soft Comput. 2012 (2012)

    Google Scholar 

  43. Wilcoxon, F.: Individual comparisons by ranking methods. In: Kotz, S., Johnson, N.L. (eds.) Breakthroughs in Statistics, pp. 196–202. Springer, Heidelberg (1992). https://doi.org/10.1007/978-1-4612-4380-9_16

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Acknowledgment

This study was supported by PNPD/CAPES (464880/2019-00) and CAPES Financial Code 001, CNPq (301618/2019-4), FAPERGS (17/2551-0000872- 3, 19/2551-0001279-9, 19/2551-0001660), and AEI/UE, FEDER (PID2019-108392GB-I00).

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Authors and Affiliations

  1. Universidade Federal do Rio Grande, Rio Grande, RS, Brazil

    Frederico B. Tiggemann, Bryan G. Pernambuco, Giancarlo Lucca, Eduardo N. Borges, Helida Santos & Graçaliz P. Dimuro

  2. Universidad Publica de Navarra, Pamplona, Navarra, Spain

    Graçaliz P. Dimuro, José A. Sanz & Humberto Bustince

Authors
  1. Frederico B. Tiggemann
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  2. Bryan G. Pernambuco
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  3. Giancarlo Lucca
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  4. Eduardo N. Borges
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  5. Helida Santos
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  6. Graçaliz P. Dimuro
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  7. José A. Sanz
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  8. Humberto Bustince
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Corresponding author

Correspondence to Bryan G. Pernambuco .

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Editors and Affiliations

  1. Federal University of São Carlos, São Carlos, Brazil

    Ricardo Cerri

  2. Federal University of ABC, Santo Andre, Brazil

    Ronaldo C. Prati

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Tiggemann, F.B. et al. (2020). An Alternative to Power Measure for Fuzzy Rule-Based Classification Systems. In: Cerri, R., Prati, R.C. (eds) Intelligent Systems. BRACIS 2020. Lecture Notes in Computer Science(), vol 12320. Springer, Cham. https://doi.org/10.1007/978-3-030-61380-8_16

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  • DOI: https://doi.org/10.1007/978-3-030-61380-8_16

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