Monte Carlo methods in fuzzy linear regression II

Abstract

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 crisp numbers, for the coefficients in the model, which minimizes one of two error measures. We use a quasi-random number generator to produce random sequences of these crisp vectors which uniformly fill the search space. We consider an example problem and show this Monte Carlo method obtains the best solution for both error measures.

Different distance measures for fuzzy linear regression with Monte Carlo methods

“…-Minimum M AE value is calculated with considering the distance measures Kaufmann and Gupta [13], Heilpern-1 [12], Heilpern-2 [12] and Chen and Hsieh [4] for interval I 0 , I 2 , I 3 and I 5 . On the other hand maximum value of M AE is calculated when the distance measure described by Abdalla and Buckley [2] is handled for the same intervals. -According to interval I 1 and I 4 , minimum values of M AE is reached with considering the distance measure described by Chen and Hsieh [4].…”

“…-According to interval I 1 and I 4 , minimum values of M AE is reached with considering the distance measure described by Chen and Hsieh [4]. However, maximum value of M AE is calculated when the distance measure described by Abdalla and Buckley [2] is taken into account.…”

“…As a result, it is proven to be the best distance measure to estimate regression model parameters with MC method for Case-III is the distance measure described by Chen and Hsieh [4]. One the other hand, distance measure used by Abdalla and Buckley [2] is not appropriate to estimate fuzzy linear regression model parameters with MC method for Case-III.…”

“…There are ten items and two independent variables in the data set. This data set is studied by Choi and Buckley [5], Dimond and Korner [8], Abdalla and Buckley [2] for comparing the proposed methods with their works. We use this data to apply different distance measures in the error measure E 1 and compare our new results with Abdalla and Buckley [2].…”

Robust Fuzzy Varying Coefficient Regression Analysis with Crisp Inputs and Gaussian Fuzzy Output

“…Besides the above-mentioned two kinds of approaches, there are some other types of approaches to solve a fuzzy regression model. For example, the Monte Carlo method can be applied to the fuzzy regression model to obtain the optimal solution within a predetermined error bound [12,13]. As a new classification technique proposed by Vapnik [14], the support vector machine (SVM) has been successful in solving pattern recognition and function estimation problems.…”