Skip to main content

Advertisement

Springer Nature Link
Log in

Continuous Linguistic Variables and Their Applications to Data Mining and Time Series Prediction

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

Membership function estimation is one of the less explored, albeit important, areas in fuzzy sets. This paper aims to define a new family of fuzzy sets called general continuous linguistic variables (GCLV), which represents a linguistic variable rather than a set of linguistic values. We refer to it as the principle of representation of linguistic variables. They are based on the well-known sigmoidal functions and contain at least three different classes of membership functions, namely, an increasing sigmoidal function, a decreasing sigmoidal function, and a convex one. These diverse features are essential to represent linguistic values exhibiting different semantics. We explore the properties of GCLV, including those ones over that allow us to approximate every continuous membership function. Finally, we illustrate the applicability of GCLV as a fuzzy tool. This leads to the development of the foundations of a new vehicle in fuzzy sets useful in data mining and time series prediction.

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
$34.99 /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

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    MATH  Google Scholar 

  2. Dombi, J.: A general class of fuzzy operators, the de morgan class of fuzzy operators and fuzziness measures induced by fuzzy operators. Fuzzy Sets Syst. 8, 149–163 (1982). https://doi.org/10.1016/0165-0114(82)90005-7

    Article  MathSciNet  MATH  Google Scholar 

  3. Dombi, J.: Membership function as an evaluation. Fuzzy Sets Syst. 35, 1–22 (1990)

    MathSciNet  MATH  Google Scholar 

  4. Bilgiç, T., Türkşen, I.B.: Measurement of membership functions theoretical and empirical work Fundamentals of fuzzy sets. Springer, Berlin (2000)

    MATH  Google Scholar 

  5. Medasani, S., Kim, J., Krishnapuram, R.: An overview of membership function generation techniques for pattern recognition. Int. J. Approx. Reason. 19, 391–417 (1998)

    MathSciNet  MATH  Google Scholar 

  6. Chung, J.H., Pak, J.M., Ahn, C.K., You, S.H., Lim, M.T., Song, M.K.: Particle filtering approach to membership function adjustment in fuzzy logic systems. Neurocomputing 237, 166–174 (2017)

    Google Scholar 

  7. Homaifar, A., McCormick, E.: Simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms. IEEE Trans. Fuzzy Syst. 3, 129–139 (1995)

    Google Scholar 

  8. Wang, C.-H., Wang, W.-Y., Lee, T.-T., Tseng, P.-S.: Fuzzy b-spline membership function (bmf) and its applications in fuzzy-neural control. IEEE Trans. Syst. Man Cybern. 25, 841–851 (1995)

    Google Scholar 

  9. Guo, H., Wang, X., Wang, L., Chen, D.: Delphi method for estimating membership function of uncertain set. J. Uncertain. Anal. Appl. 4, 3 (2016)

    Google Scholar 

  10. Valente-de Oliveira, J.: Semantic constraints for membership function optimization. IEEE Trans. Syst. Man Cybern. 29, 128–138 (1999)

    Google Scholar 

  11. Miller, G.A.: The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychol. Rev. 63(2), 81–97 (1956)

    Google Scholar 

  12. Drakopoulos, J.A.: Sigmoidal theory. Fuzzy Sets Syst. 76, 349–363 (1995)

    MathSciNet  MATH  Google Scholar 

  13. Drakopoulos, J.A., Hayes-Roth, B.: tfpr: A fuzzy and structural pattern recognition system of multi-variate time-dependent pattern classes based on sigmoidal functions. Fuzzy Sets and Systems 99, 57–72 (1998)

    Google Scholar 

  14. Cybenko, G.: Approximation by superpositions of a sigmoidal function. Math. Control Signals Syst. 2, 303–314 (1989)

    MathSciNet  MATH  Google Scholar 

  15. Narayanan, S.J., Paramasivam, I., Bhatt, R.B., Khalid, M.: A study on the approximation of clustered data to parameterized family of fuzzy membership functions for the induction of fuzzy decision trees. Cybern. Inf. Technol. 15, 75–96 (2015)

    Google Scholar 

  16. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, New York (2000)

    MATH  Google Scholar 

  17. Bartle, R.G.: The elements of real analysis. Wiley, New York (1964)

    MATH  Google Scholar 

  18. Jang, J.-S.R., Sun, C.-T., Mizutani, E.: Neuro-fuzzy and Soft Computing. A computational approach to learning and machine intelligence. Prentice Hall Inc, New York (1997)

    Google Scholar 

  19. Pedrycz, W., Reformat, M., Li, K.J.: Or/and neurons and the development of interpretable logic models. IEEE Trans. Neural Netw. 17, 636–658 (2006)

    Google Scholar 

  20. Reyes-Galaviz, O.F., Pedrycz, W.: Fuzzy relational structures: Learning alternatives for fuzzy modeling. In IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), pp. 374–379. Joint. IEEE, (2013)

  21. Espín-Andrade, R.A., González-Caballero, E., Pedrycz, W., Fernández-González, E.R.: Archimedean-compensatory fuzzy logic systems. Int. J. Comput. Intellig. Syst. 8(sup2), 54–62 (2015)

    Google Scholar 

  22. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-I. Inf. Sci. 8, 199–249 (1975)

    MathSciNet  MATH  Google Scholar 

  23. Mencar, C., Castellano, G., Fanelli, A.M.: Some fundamental interpretability issues in fuzzy modeling. Joint EUSFLAT-LFA, pp. 100–105. Springer, Berlin (2005)

    Google Scholar 

  24. Mamdani, E.H., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller. Int. J. Man-Mach. Stud. 7, 1–13 (1975)

    MATH  Google Scholar 

  25. Alonso, J.M., Magdalena, L., Guillaume, S.: Hilk: a new methodology for designing highly interpretable linguistic knowledge bases using the fuzzy logic formalism. Int. J. Intellig. Syst. 23, 761–794 (2008)

    MATH  Google Scholar 

  26. Espinosa, J., Vandewalle, J.: Constructing fuzzy models with linguistic integrity from numerical data-afreli algorithm. IEEE Trans. Fuzzy Syst. 8(5), 591–600 (2000)

    Google Scholar 

  27. Guillaume, S., Charnomordic, B.: Generating an interpretable family of fuzzy partitions from data. IEEE Trans. Fuzzy Syst. 3(12), 324–335 (2004)

    Google Scholar 

  28. Bezdek, J.C., Harris, J.D.: Fuzzy partitions and relations; an axiomatic basis for clustering. Fuzzy Sets Syst. 1, 111–127 (1978)

    MathSciNet  MATH  Google Scholar 

  29. Krzysztof, C.: Design of Interpretable Fuzzy Systems. Springer, Berlin (2017)

    Google Scholar 

  30. Alonso, J.M., Magdalena, L., González-Rodríguez, G.: Looking for a good fuzzy system interpretability index: an experimental approach. Int. J. Approx. Reason. 51, 115–134 (2009)

    MathSciNet  Google Scholar 

  31. Zwick, R., Carlstein, E., Budescu, D.V.: Measures of similarity among fuzzy concepts: a comparative analysis. Int. J. Approx. Reason. 12, 221–242 (1987)

    MathSciNet  Google Scholar 

  32. Koczy, L., Hirota, K.: Ordering, distance and closeness of fuzzy sets. Fuzzy Sets Syst. 59, 281–293 (1993)

    MathSciNet  MATH  Google Scholar 

  33. Subasic, P., Hirota, K.: Similarity rules and gradual rules for analogical interpolative reasoning with imprecise data. Fuzzy Sets Syst. 96, 53–75 (1998)

    MathSciNet  Google Scholar 

  34. Herrera, F., Martínez, L.: A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans. Fuzzy Syst. 8, 746–752 (2000)

    Google Scholar 

  35. González-Caballero, E., Díaz-Vázquez, S., Espín-Andrade, R.A., Montes-Rodríguez, S.: New measures of similarity based on fuzzy implications. J. Intellig. Fuzzy Syst. 33(6), 3493–3503 (2017)

    Google Scholar 

  36. Herrera, F., Herrera-Viedma, E., Martínez, L.: A fuzzy linguistic methodology to deal with unbalanced linguistic term sets. IEEE Trans. Fuzzy Syst. 16(2), 354–370 (2008)

    Google Scholar 

  37. Bodenhofer, U., Bauer, P.: A formal model of interpretability of linguistic variables. Interpretability Issues in Fuzzy Modeling, pp. 524–545. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  38. Asuncion, A., Newman, D.: Uci machine learning repository (2007)

  39. Cortez, P., Cerdeira, A., Almeida, F., Matos, T., Reis, J.: Modeling wine preferences by data mining from physicochemical properties. Decis. Support Syst. 47, 547–53 (2009)

    Google Scholar 

  40. Ceruto, T., Rosete, A., Espín, R.A.: Knowledge discovery by fuzzy predicates. Soft computing for business intelligence, pp. 187–196. Springer, Berlin (2014)

    Google Scholar 

  41. Espín-Andrade, R.A., González, E., Pedrycz, W., Fernández, E.: An interpretable logical theory: The case of compensatory fuzzy logic. International Journal of Computational Intelligence Systems 9, 612–626 (2016)

    Google Scholar 

  42. Martínez, M., Espín, R.A., López, V., Rosete, A.: Discovering knowledge by fuzzy predicates in compensatory fuzzy logic using metaheuristic algorithms. Soft computing for business intelligence, pp. 161–174. Springer, Berlin (2014)

    Google Scholar 

  43. Herrera, F., Carmona, C.J., González, P., del Jesús, M.J.: An overview on subgroup discovery: foundations and applications. Knowl. Inf. Syst. 29, 495–525 (2010)

    Google Scholar 

  44. Kiang, M.: A comparative assessment of classification methods. Decision Support Syst. 35, 441–454 (2003)

    Google Scholar 

  45. Box, G.E.P., Jenkins, G.M., Reinsel, G.C.: Time series analysis: forecasting and control. Prentice-Hall International Inc, New Jersey (1994)

    MATH  Google Scholar 

  46. Schloegl, A.: The electroencephalogram and the adaptive autoregressive model: theory and applications. Shaker, Aachen (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technical University of Havana, 27 Calle 114 # 11901 e/ Ciclovía y Rotonda, Marianao, Havana, Cuba

    Erick González-Caballero

  2. Autonomous University of Coahuila, Blvd Revolución No 151 Oriente, Torreón, Coahuila, Mexico

    Rafael A. Espín-Andrade

  3. University of Alberta Edmonton, Edmonton, AB, T6R 2V4, Canada

    Witold Pedrycz

  4. King Abdulaziz University Jeddah, 21589, Jeddah, Saudi Arabia

    Witold Pedrycz

  5. Systems Research Institute, Polish Academy of Sciences Warsaw, Warsaw, Poland

    Witold Pedrycz

  6. University of Jaén, 23071, Jaén, Spain

    Luis Martínez

  7. Autonomous University of Coahuila, Blvd Revolución No 151 Oriente, Torreón, Coahuila, Mexico

    Liliana A. Guerrero-Ramos

Authors
  1. Erick González-Caballero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rafael A. Espín-Andrade
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Witold Pedrycz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Luis Martínez
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Liliana A. Guerrero-Ramos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Erick González-Caballero.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

González-Caballero, E., Espín-Andrade, R.A., Pedrycz, W. et al. Continuous Linguistic Variables and Their Applications to Data Mining and Time Series Prediction. Int. J. Fuzzy Syst. 23, 1431–1452 (2021). https://doi.org/10.1007/s40815-020-00968-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-020-00968-w

Keywords

Search

Navigation