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Monte Carlo methods in fuzzy linear regression. (English) Zbl 1117.62067

Summary: We apply our new fuzzy Monte Carlo method to a certain fuzzy linear regression problem to estimate the best solution. The best solution is a vector of triangular fuzzy numbers, for the fuzzy coefficients in the model, which minimizes one of two error measures. We use a quasi-random number generator to produce random sequences of these fuzzy vectors which uniformly fill the search space. We consider an example problem and show that this Monte Carlo method obtains the best solution for one error measure and is approximately best for the other error measure.

MSC:

62J05 Linear regression; mixed models
65C05 Monte Carlo methods
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References:

[1] Choi SH, Buckley JJ (2007) Fuzzy regression using least absolute deviation estimators. Soft Comput (to appear)
[2] Buckley, JJ; Eslami, E., Introduction to fuzzy logic and fuzzy sets (2002), Heidelberg: Springer, Heidelberg · Zbl 0985.03002
[3] Buckley, JJ, Monte Carlo studies with random fuzzy numbers (2007), Heidelberg (to appear): Springer, Heidelberg (to appear)
[4] Cheng C-B (2001) Fuzzy regression analysis by a fuzzy neural network and its application to dual response optimization. In: Proceedings joint 9th IFSA World congress and 20th NAFIPS international Conference, Vancouver, Canada, Vol 5, pp 2681-2686
[5] D’Urso, P., Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data, Comput Stat Data Anal, 42, 47-72 (2003) · Zbl 1429.62337 · doi:10.1016/S0167-9473(02)00117-2
[6] Feuring T, Golubski W, Gassmann M (2000) Fuzzy regression: a genetic programming approach. In: Fourth international Conference knowledge-based intelligent engineering systems and allied technologies, Aug 30-Sept 1, Brighton, UK
[7] Henderson SG, Chiera BA, Cooke RM (2000) Generating “dependent” quasi-random numbers. In: Proceedings of the 2000 winter simulation conference, Orlando, FL, Dec 10-13, pp 527-536
[8] Hogg, RV; Tanis, EA, Probability and statistical inference (2001), Upper Saddle River: Prentice Hall, Upper Saddle River
[9] Kim, B.; Bishu, RR, Evaluation of fuzzy linear regression models by comparing membership functions, Fuzzy Sets Syst, 100, 343-352 (1998) · doi:10.1016/S0165-0114(97)00100-0
[10] Lindgren, BW, Statistical theory (1976), New York: MacMillan, New York · Zbl 0322.62002
[11] Press WH, Flannery BP, Teukolsky SA, Vetterling WT (2002): Numerical recipes in C: the art of scientific computing, 6th edn. Cambridge University Press, Cambridge · Zbl 1078.65500
[12] Savic, DA; Pedryzc, W., Evaluation of fuzzy linear regression models, Fuzzy Sets Syst, 39, 51-63 (1991) · Zbl 0714.62065 · doi:10.1016/0165-0114(91)90065-X
[13] Tanaka, H., Fuzzy data analysis by possibilistic linear regression models, Fuzzy Sets Syst, 24, 363-375 (1987) · Zbl 0633.93060 · doi:10.1016/0165-0114(87)90033-9
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