The aim of this study was 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 (Introduction to fuzzy arithmetic theory and applications. Van Nostrand Reinhold, New York, 1991), Heilpern-2 (Fuzzy Sets Syst 91(2):259–268, 1997) and Chen and Hsieh (Aust J Intell Inf Process Syst 6(4):217–229, 2000). One the other hand, the worst distance measure is the distance measure used by Abdalla and Buckley (Soft Comput 11:991–996, 2007; Soft Comput 12:463–468, 2008). These results would be useful to enrich the studies that have already focused on fuzzy linear regression models.
Fuzzy linear regression Fuzzy distance measure Monte Carlo
Compliance with ethical standards
Conflict of interest
Author Duygu İçen declares that she has no conflict of interest. Author Marco Cattaneo declares that he has no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
Roh SB, Ahn TC, Pedrycz W (2012) Fuzzy linear regression based on polynomial neural networks. Expert Syst Appl 39:8909–8928CrossRefGoogle Scholar
Sadi-Nezhad S, Khalili Damghani K (2010) Application of a fuzzy TOPSIS method base on modified preference ratio and fuzzy distance measurement in assessment of traffic police centers performance. Appl Soft Comput 10:1028–1039CrossRefGoogle Scholar