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

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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.

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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

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  1. Erick González-Caballero
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  2. Rafael A. Espín-Andrade
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  3. Witold Pedrycz
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  4. Luis Martínez
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  5. Liliana A. Guerrero-Ramos
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Correspondence to Erick González-Caballero.

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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

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

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