Different distance measures for fuzzy linear regression with Monte Carlo methods

Abstract

The aim of this study is to determine the best distance measure for estimating the fuzzy linear regression model parameters with Monte Carlo (MC) methods. It is pointed out that only one distance measure is used for fuzzy linear regression with MC methods within the literature. Therefore, three different definitions of distance measure between two fuzzy numbers are introduced. Estimation accuracies of existing and proposed distance measures are explored with the simulation study. Distance measures are compared to each other in terms of estimation accuracy; hence this study demonstrates that the best distance measures to estimate fuzzy linear regression model parameters with MC methods are the distance measures defined by Kaufmann and Gupta [13], Heilpern-2 [12] and Chen and Hsieh [4]. One the other hand, the worst distance measure is the distance measure used by Abdalla and Buckley [1][2]. These results would be useful to enrich the studies that have already focused on fuzzy linear regression models.

Derivative-based acceleration of general vector machine

“…Buckley (2007, 2008) applied their fuzzy MC method in solving linear regression problems. By using MC method, Duygu and Cattaneo (2016) researched the way to determine the best parameters of fuzzy linear regression. Freitas et al (2000) proposed a strategy for training NNs with MC algorithm.…”