مقاله انگلیسی رایگان در مورد رگرسیون خطی امکانی با داده های فازی – الزویر 2018

Basically, there are two concepts to fuzzy linear regression. The first one is based on the model (1) with random error terms. The objective is usually to minimize the total sum of squares of the errors, extending the least squares method to the fuzzy environment. One of the early works was Diamond [2]. Later, it was extended by many authors including Cern´y et al. [3] for enclosing ˇ the set of least square solutions of interval data, Gu et al. [4] for an improved regression method proving statistical properties known for the crisp case, D’Urso [5] for constrained and unconstrained estimation, or D’Urso & Gastaldi [6] and Muzzioli et al. [7] for an extension to polynomial fuzzy regression. Interval data can be understood either in the ontic or epistemic sense [8]. Since fuzzy data can be understood as generalized interval data [40], they inherit one of the interpretations, too. In the epistemic interpretation of interval data, an interval is a model for imprecise information about a real number which is not known exactly but can bounded both from above and from below. In the ontic interpretation, an interval represents a precise entity and data are intrinsically given by intervals. The results of this paper – which studied properties of estimation methods for regression models – do not lean on the first or the latter interpretation of data. However, the interpretation of data is essential for the choice of the regression methodology. We study the possibilistic regression. This methodology is suitable namely for epistemic data since the possibilistic paradigm takes into account all possible realizations of the real-valued data in the observed intervals.