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Fuzzy Regression Analysis: An Actuarial Perspective

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Fuzzy Statistical Decision-Making

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 343))

Abstract

The first objective of this paper is to describe from a critical point of view the main types of fuzzy regression methods: those based on minimum fuzziness principle, those that are built up by minimising the squared distance between observations and estimates and models that mix both methodologies. Finally, we revise the actuarial applications of fuzzy regression proposed in the literature and develop in detail two of them: estimating the yield curve and calculating claim reserves.

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References

  1. Dubois, D., Prade, H.: Foreword. In: Kacprzyk, J., Fedrizzi, M. (eds.) Fuzzy Regression Analysis. Physica-Verlag, Heidelberg (1992)

    Google Scholar 

  2. McCauley-Bell, P., Wang, H.: Fuzzy linear regression models for assessing risks of cumulative trauma disorders. Fuzzy Sets Syst. 92, 317–340 (1997)

    Article  MathSciNet  Google Scholar 

  3. Lee, H.T., Chen, S.H.: Fuzzy regression model with fuzzy input and output data for manpower forecasting. Fuzzy Sets Syst. 119, 205–213 (2001)

    Article  MathSciNet  Google Scholar 

  4. Ramenazi, R., Duckstein, L.: Fuzzy regression analysis of the effect of university research on regional technologies. In: Kacprzyk, J., Fedrizzi, M. (eds.) Fuzzy Regression Analysis, pp. 237–263. Physica-Verlag, Heidelberg (1992)

    Google Scholar 

  5. Watada, J.: Fuzzy time-series analysis and forecasting of sales volume. In: Kacprzyk, J., Fedrizzi, M. (eds.) Fuzzy Regression Analysis, pp. 211–227. Physica-Verlag, Heidelberg (1992)

    Google Scholar 

  6. Profillidis, V.A., Papadopoulos, B.K., Botzoris, G.N.: Similarities in fuzzy regression models and application on transportation. Fuzzy Econ. Rev. 4(1), 83–98 (1999)

    Google Scholar 

  7. Tseng, F.-M., Tzeng, G.-H., Yu, H.-C., Yuan, B.J.-C.: Fuzzy ARIMA model for forecasting the foreign exchange market. Fuzzy Sets Syst. 118, 9–19 (2001)

    Article  MathSciNet  Google Scholar 

  8. Chang, Y.-H.O., Ayyub, B.M.: Fuzzy regression methods-a comparative assessment. Fuzzy Sets Syst. 119, 187–203 (2001)

    Article  MathSciNet  Google Scholar 

  9. Tanaka, H.: Fuzzy data analysis by possibility linear models. Fuzzy Sets Syst. 24, 363–375 (1987)

    Article  MATH  Google Scholar 

  10. Tanaka, H., Ishibuchi, H.: A possibilistic regression analysis based on linear programming. In: Kacprzyk, J., Fedrizzi, M. (eds.) Fuzzy Regression Analysis, pp. 47–60. Physica-verlag, Heidelberg (1992)

    Google Scholar 

  11. Chang, Y.-H.O.: Hybrid fuzzy least-squares regression analysis and its reliability measures. Fuzzy Sets Syst. 119, 225–246 (2001)

    Google Scholar 

  12. Ishibuchi, H., Nii, M.: Fuzzy regression using asymmetric fuzzy coefficients and fuzzified neural networks. Fuzzy Sets Syst. 119, 273–290 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  13. Savic, D., Predrycz, W.: Fuzzy linear models: construction and evaluation. In: Kacprzyk, J., Fedrizzi, M. (eds.) Fuzzy Regression Analysis, pp. 91–100. Physica-Verlag, Heidelberg (1992)

    Google Scholar 

  14. Buckley, J.J., Qu, Y.: On using & α-cuts to evaluate fuzzy equations. Fuzzy Sets Syst. 38, 309–312 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  15. Diamond, P.: Fuzzy least squares. Inf. Sci. 46, 141–157 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  16. Andrés, J., Terceño, A.: Applications of fuzzy regression in actuarial analysis. J. Risk Insur. 70(4), 665–699 (2003)

    Article  Google Scholar 

  17. Berry-Stölze, T.R., Koissi, M.-C., Shapiro, A.F.: Detecting fuzzy relationships in regression models: the case of insurer surveillance in Germany. Insur.: Math. Econ. 46(3), 554–567 (2010)

    MathSciNet  MATH  Google Scholar 

  18. McCulloch, J.H.: The tax-adjusted yield curve. J. Finance 30, 811–829 (1975)

    Article  Google Scholar 

  19. Shapiro, A.F.: Fuzzy regression and the term structure of interest rates revisited. In: 14th Annual International AFIR Colloquium, Boston (2004b). http://afir2004.soa.org/afir_papers.htm

  20. Hung, W.-L., Yan, M.-S.: An omission approach for detecting outliers in fuzzy regression. Fuzzy Sets Syst. 157, 3109–3122 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  21. Chen, Y.-S.: Outliers detection and confidence interval modification in fuzzy regression. Fuzzy Sets Syst. 119, 259–272 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  22. Hojati, M., Bector, C.R., Smimou, K.: A simple method for computation of fuzzy linear regresion. Eur. J. Oper. Res. 166, 172–184 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  23. Moskowitz, J.J., Kim, Y.: On assessing H-value on fuzzy linear regression. Fuzzy Sets Syst. 58(3), 303–327 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  24. Koissi, M.C., Shapiro, A.F.: The temporal structure of interest rates. A least squares approach. ARCH (2009)

    Google Scholar 

  25. Apaydin, A., Baser, F.: Hybrid fuzzy least-squares regression analysis in claims reserving with geometric separation method. Insur.: Math. Econ. 47, 113–122 (2010)

    MathSciNet  MATH  Google Scholar 

  26. Taylor, G.: Claims Reserving in Non-life Insurance. North-Holland, Amsterdam (1986)

    MATH  Google Scholar 

  27. de Andrés Sánchez, J., Gómez, A.T.: Estimating a term structure of interest rates for fuzzy financial pricing by using fuzzy regression methods. Fuzzy Sets Syst 139(2), 399–424 (2003)

    Google Scholar 

  28. Koissi, M.C., Shapiro, A.F.: Fuzzy formulation of the lee-carter model for mortality forecasting. Insur.: Math. Econ. 39, 287–309 (2006)

    MathSciNet  MATH  Google Scholar 

  29. de Andrés, J.: Calculating insurance claim reserves with fuzzy regression. Fuzzy Sets Syst. 157(23), 3091–3108 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  30. de Andrés-Sánchez, J.: Claim reserving with fuzzy regression and the two ways of ANOVA. Applied Soft Computing, 12(8), 2435–2441 (2012)

    Google Scholar 

  31. Kremer, E.: IBNR claims and the two way model of ANOVA. Scandinavian Actuarial J, 1, 47–55 (1982)

    Google Scholar 

  32. Kaufmann, A.: Fuzzy subsets applications in O.R. and management. In: Jones, A., Kaufmann, A., Zimmermann, H.-J. (eds.) Fuzzy Set Theory and Applications, pp. 257–300. Reidel, Dordretch (1986)

    Google Scholar 

  33. Buckley, J.J.: The fuzzy mathematics of finance. Fuzzy Sets Syst. 21, 57–73 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  34. Li, M.: Calzi. towards a general setting for the fuzzy mathematics of finance. Fuzzy Sets Syst. 35, 265–280 (1990)

    Article  MATH  Google Scholar 

  35. Ostaszewski, K.: An Investigation into Possible Applications of Fuzzy Sets Methods in Actuarial Science. Society of Actuaries, Schaumburg (USA) (1993)

    Google Scholar 

  36. Cummins, J.D., Derrig, R.A.: Fuzzy financial pricing of property-liability insurance. North Am. Actuarial J. 1, 21–44 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  37. Echols, M.E., Elliott, J.W.: A Quantitative yield curve for estimating the term structure of interest rates. J. Financ. Quant. Anal. 11, 87–114 (1976)

    Article  Google Scholar 

  38. Straub, E.: Non-life insurance mathematics. Springerm, Berlin (1997)

    MATH  Google Scholar 

  39. Sherman, R.E.: Extrapolating, smoothing and Interpolating development factors. Proc. Casualty Actuarial Soc. 71, 122–123 (1984)

    Google Scholar 

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Authors and Affiliations

  1. Social and Business Research Laboratory, Rovira i Virgili University, Tarragona, Spain

    Jorge de Andrés-Sánchez

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  1. Jorge de Andrés-Sánchez
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Correspondence to Jorge de Andrés-Sánchez .

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Editors and Affiliations

  1. Management Faculty, Industrial Engineering Department, Istanbul Technical University, Istanbul, Turkey

    Cengiz Kahraman

  2. Management Facult, Industrial Engineering Department, Istanbul Technical University, Istanbul, Turkey

    Özgür Kabak

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de Andrés-Sánchez, J. (2016). Fuzzy Regression Analysis: An Actuarial Perspective. In: Kahraman, C., Kabak, Ö. (eds) Fuzzy Statistical Decision-Making. Studies in Fuzziness and Soft Computing, vol 343. Springer, Cham. https://doi.org/10.1007/978-3-319-39014-7_11

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  • DOI: https://doi.org/10.1007/978-3-319-39014-7_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-39012-3

  • Online ISBN: 978-3-319-39014-7

  • eBook Packages: EngineeringEngineering (R0)

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