Fuzzy Random Regression to Improve Coefficient Determination in Fuzzy Random Environment

Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 287)


Determining the coefficient value is important to measure relationship in algebraic expression and to build a mathematical model though it is complex and troublesome. Additionally, providing precise value for the coefficient is difficult when it deals with fuzzy information and the existence of random information increase the complexity of deciding the coefficient. Hence, this paper proposes a fuzzy random regression method to estimate the coefficient values for which statistical data contains simultaneous fuzzy random information. A numerical example illustrates the proposed solution approach whereby coefficient values are successfully deduced from the statistical data and the fuzziness and randomness were treated based on the property of fuzzy random regression. The implementation of the fuzzy random regression method shows the significant capabilities to estimate the coefficient value to further improve the model setting of production planning problem which retain simultaneous uncertainties.


Coefficient fuzzy random variable fuzzy random regression 


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  1. 1.
    Smith, T.F., Waterman, M.S.: Identification of Common Molecular Subsequences. J. Mol. Biol. 147, 195–197 (1981)CrossRefGoogle Scholar
  2. 2.
    May, P., Ehrlich, H.C., Steinke, T.: ZIB Structure Prediction Pipeline: Composing a Complex Biological Workflow through Web Services. In: Nagel, W.E., Walter, W.V., Lehner, W. (eds.) Euro-Par 2006. LNCS, vol. 4128, pp. 1148–1158. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Foster, I., Kesselman, C.: The Grid: Blueprint for a New Computing Infrastructure. Morgan Kaufmann, San Francisco (1999)Google Scholar
  4. 4.
    Czajkowski, K., Fitzgerald, S., Foster, I., Kesselman, C.: Grid Information Services for Distributed Resource Sharing. In: 10th IEEE International Symposium on High Performance Distributed Computing, pp. 181–184. IEEE Press, New York (2001)CrossRefGoogle Scholar
  5. 5.
    Foster, I., Kesselman, C., Nick, J., Tuecke, S.: The Physiology of the Grid: an Open Grid Services Architecture for Distributed Systems Integration. Technical report, Global Grid Forum (2002)Google Scholar
  6. 6.
    National Center for Biotechnology Information,, Montgomery, D.C., Peck, E.A., Vining, G.G.: Introduction to linear regression analysis, vol. 821. Wiley (2012)
  7. 7.
    Griffiths, T.L., Tenenbaum, J.B.: Predicting the future as Bayesian inference: People combine priorknowledge with observations when estimating duration and extent 140(4), 725–743 (2011)Google Scholar
  8. 8.
    Cave, W.C.: Prediction Theory for Control System (2011)Google Scholar
  9. 9.
    Yang, M.S., Ko, C.H.: On cluster-wise fuzzy regression analysis. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 27(1), 1–13 (1997)CrossRefGoogle Scholar
  10. 10.
    González-Rodríguez, G., Blanco, Á., Colubi, A., Lubiano, M.A.: Estimation of a simple linear regression model for fuzzy random variables. Fuzzy Sets and Systems 160(3), 357–370 (2009)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Watada, J.: Building models based on environment with hybrid uncertainty. In: 2011 4th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO), pp. 1–10. IEEE (April 2011)Google Scholar
  12. 12.
    Nureize, A., Watada, J.: Multi-level multi-objective decision problem through fuzzy random regression based objective function. In: 2011 IEEE International Conference on Fuzzy Systems (FUZZ), pp. 557–563. IEEE (June 2011)Google Scholar
  13. 13.
    Watada, J., Wang, S., Pedrycz, W.: Building confidence-interval-based fuzzy random regression models. IEEE Transactions on Fuzzy Systems 17(6), 1273–1283 (2009)CrossRefGoogle Scholar
  14. 14.
    Näther, W.: Regression with fuzzy random data. Computational Statistics & Data Analysis 51(1), 235–252 (2006)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Kwakernaak: Fuzzy random variables—I. Definitions and Theorems. Information Sciences 15(1), 1–29 (1978)Google Scholar
  16. 16.
    Market Watch 2012. The Rubber Sector in Malaysia, (retrieved October 22, 2013)
  17. 17.
    Malaysian Investment Development Authority. Rubber-based industry, (retrieved on October 10, 2013)
  18. 18.
    Malaysian Rubber Export Promotion Council, (retrieved on October 10, 2013)
  19. 19.
    Malaysian Rubber Board.Natural Rubber Statistic, (retrieved September 1, 2013)

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Faculty of Computer Science and Information TechnologyUniversiti Tun Hussein OnnBatu PahatMalaysia

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