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A possibilistic approach to latent structure analysis for symmetric fuzzy data

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  • D'Urso, Pierpaolo
  • Giordani, Paolo

Abstract

In many situations the available amount of data is huge and can be intractable. When the data set is single valued, latent structure models are recognized techniques, which provide a useful compression of the information. This is done by considering a regression model between observed and unobserved (latent) fuzzy variables. In this paper, an extension of latent structure analysis to deal with fuzzy data is proposed. Our extension follows the possibilistic approach, widely used both in the cluster and regression frameworks. In this case, the possibilistic approach involves the formulation of a latent structure analysis for fuzzy data by optimization. Specifically, a non-linear programming problem in which the fuzziness of the model is minimized is introduced. In order to show how our model works, the results of two applications are given.

Suggested Citation

  • D'Urso, Pierpaolo & Giordani, Paolo, 2003. "A possibilistic approach to latent structure analysis for symmetric fuzzy data," Economics & Statistics Discussion Papers esdp03014, University of Molise, Department of Economics.
    • Handle: RePEc:mol:ecsdps:esdp03014
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    References listed on IDEAS

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    1. Cheng, Ching-Hsue & Yang, Kuo-Lung & Hwang, Chia-Lung, 1999. "Evaluating attack helicopters by AHP based on linguistic variable weight," European Journal of Operational Research, Elsevier, vol. 116(2), pages 423-435, July.
    2. D'Urso, Pierpaolo, 2003. "Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 47-72, February.
    3. Coppi, Renato & D'Urso, Pierpaolo, 2003. "Three-way fuzzy clustering models for LR fuzzy time trajectories," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 149-177, June.
    4. Cheng, Ching-Hsue & Lin, Yin, 2002. "Evaluating the best main battle tank using fuzzy decision theory with linguistic criteria evaluation," European Journal of Operational Research, Elsevier, vol. 142(1), pages 174-186, October.
    5. Giordani, Paolo & Kiers, Henk A. L., 2004. "Principal Component Analysis of symmetric fuzzy data," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 519-548, April.
    6. Hougaard, Jens Leth, 1999. "Fuzzy scores of technical efficiency," European Journal of Operational Research, Elsevier, vol. 115(3), pages 529-541, June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Latent structure analysis; symmetric fuzzy data set; possibilistic approach.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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