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A fuzzy regression model based on distances and random variables with crisp input and fuzzy output data: a case study in biomass production

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Abstract

Least-squares technique is well-known and widely used to determine the coefficients of a explanatory model from observations based on a concept of distance. Traditionally, the observations consist of pairs of numeric values. However, in many real-life problems, the independent or explanatory variable can be observed precisely (for instance, the time) and the dependent or response variable is usually described by approximate values, such as “about \(\pounds300\)” or “approximately $500”, instead of exact values, due to sources of uncertainty that may affect the response. In this paper, we present a new technique to obtain fuzzy regression models that consider triangular fuzzy numbers in the response variable. The procedure solves linear and non-linear problems and is easy to compute in practice and may be applied in different contexts. The usefulness of the proposed method is illustrated using simulated and real-life examples.

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Acknowledgments

We are grateful to the referees for their constructive comments which lead to improvements in the paper. This paper has been partially supported by the Junta de Andalucía and projects FQM-245, FQM-268, FQM-178 of the Andalusian CICYE, Spain.

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Authors and Affiliations

  1. Department of Statistics and Operations, University of Jaén, Las Lagunillas s/n, Jaén, Spain

    C. Roldán & A. Roldán

  2. Department of Mathematics, University of Jaén, Las Lagunillas s/n, Jaén, Spain

    J. Martínez-Moreno

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  1. C. Roldán
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  2. A. Roldán
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  3. J. Martínez-Moreno
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Correspondence to C. Roldán.

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Roldán, C., Roldán, A. & Martínez-Moreno, J. A fuzzy regression model based on distances and random variables with crisp input and fuzzy output data: a case study in biomass production. Soft Comput 16, 785–795 (2012). https://doi.org/10.1007/s00500-011-0769-1

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