A weighted goal programming approach to estimate the linear regression model in full quasi type-2 fuzzy environment

Issue title: Selected papers from the 4th Iranian Joint Congress On Fuzzy and Intelligent Systems – CFIS2015, 9–11 September 2015

Article type: Research Article

Authors: Hosseinzadeh, Elham^a | Hassanpour, Hassan^{a; *} | Arefi, Mohsen^b

Affiliations: [a] Department of Mathematics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand, Iran | [b] Department of Statistics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand, Iran

Correspondence: [*] Corresponding author. Hassan Hassanpour, Department of Mathematics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand, Iran. Tel.: +98 56 32202301; Fax: +98 56 32202041; E-mail: hhassanpour@birjand.ac.ir.

Abstract: This study attempts to develop a quasi type-2 fuzzy regression model in full quasi type-2 fuzzy environment. To estimate the parameters of the proposed model, first, a weighted distance between quasi type-2 fuzzy numbers is defined based on L1-norm. Then some approximations for multiplication of two quasi type-2 fuzzy numbers (QT2FNs) are introduced. The problem of estimation of the parameters relies on a non-linear optimization problem, which is converted to a linear optimization problem. The method can handel both symmetric and asymmetric data. Two real world examples demonstrate the feasibility and efficiency of the proposed method. The predictive performance of the model is examined by cross-validation, and a similarity measure is used to compare our model with a similar model.

Keywords: Fuzzy linear regression, goal programming, type-2 fuzzy set, uncertainty, quasi type-2 fuzzy number

DOI: 10.3233/IFS-152046

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 3, pp. 1319-1330, 2016