Different distance measures for fuzzy linear regression with Monte Carlo methods

Cattaneo, Marco E.G.V.; İçen, Duygu

Abstract

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.

Citation

Cattaneo, M. E., & İçen, D. (2017). Different distance measures for fuzzy linear regression with Monte Carlo methods. Soft Computing, 21(22), 6687-6697. https://doi.org/10.1007/s00500-016-2218-7

• Journal Article Type: Article
• Acceptance Date: Jun 2, 2016
• Online Publication Date: Jun 13, 2016
• Publication Date: 2017-10
• Deposit Date: Jun 16, 2016
• Publicly Available Date: Jun 16, 2016
• Journal: Soft computing
• Print ISSN: 1432-7643
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 21
• Issue: 22
• Pages: 6687-6697
• DOI: https://doi.org/10.1007/s00500-016-2218-7
• Keywords: Fuzzy linear regression, Fuzzy distance measure, Monte Carlo
• Public URL: https://hull-repository.worktribe.com/output/439745
• Publisher URL: http://link.springer.com/article/10.1007/s00500-016-2218-7
• Additional Information: Authors' accepted manuscript of article published in: Soft computing, 2017, issue 22.
• Contract Date: Jun 16, 2016