Monte Carlo methods in fuzzy linear regression

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 this Monte Carlo method obtains the best solution for one error measure and is approximately best for the other error measure.

[1]  James J. Buckley,et al.  Fuzzy regression using least absolute deviation estimators , 2007, Soft Comput..

[2]  H. Tanka Fuzzy data analysis by possibilistic linear models , 1987 .

[3]  Ram R. Bishu,et al.  Evaluation of fuzzy linear regression models by comparing membership functions , 1998, Fuzzy Sets Syst..

[4]  Pierpaolo D'Urso,et al.  Linear regression analysis for fuzzy = crisp input and fuzzy = crisp output data , 2015 .

[5]  Areeg Said Abdalla Monte Carlo studies with random fuzzy numbers , 2006 .

[6]  Roger M. Cooke,et al.  Generating "dependent" quasi-random numbers , 2000, 2000 Winter Simulation Conference Proceedings (Cat. No.00CH37165).

[7]  Witold Pedrycz,et al.  Evaluation of fuzzy linear regression models , 1991 .

[8]  Chi-Bin Cheng Fuzzy regression analysis by a fuzzy neural network and its application to dual response optimization , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[9]  Thomas Feuring,et al.  Fuzzy regression: a genetic programming approach , 2000, KES'2000. Fourth International Conference on Knowledge-Based Intelligent Engineering Systems and Allied Technologies. Proceedings (Cat. No.00TH8516).

[10]  Ranjan Vepa,et al.  INTRODUCTION TO FUZZY LOGIC AND FUZZY SETS , 1992 .