Abstract
We introduce a new fuzzy linear regression method. The method is capable of approximating fuzzy relationships between an independent and a dependent variable. The independent and dependent variables are expected to be a real value and triangular fuzzy numbers, respectively. We demonstrate on twenty datasets that the method is reliable, and it is less sensitive to outliers, compare with possibilistic-based fuzzy regression methods. Unlike other commonly used fuzzy regression methods, the presented method is simple for implementation and it has linear time-complexity. The method guarantees non-negativity of model parameter spreads.
Highlights
A regression model approximates the functional relationship between a dependent y and independent variables x
Statistical regression models are most often used for this purpose, but their usage is limited by an assumption that any deviation of a prediction from a corresponding observation is due to a random error
We demonstrated in the numerical examples that the proposed Boscovich fuzzy regression line (BFRL) is capable of approximating a fuzzy linear relationship between the dependent y and one independent variable x, where the independent variable is a real value number and the dependent variable is a triangular fuzzy number Y
Summary
A regression model approximates the functional relationship between a dependent y and independent variables x. Statistical regression models are most often used for this purpose, but their usage is limited by an assumption that any deviation of a prediction from a corresponding observation is due to a random error. The deviations are a result of imprecise observations, an indefiniteness of the system structure and parameters [1,2], or the vagueness of human perception of the model (in contrast with the statistical regression where the errors are associated with observations) [3]. There are cases where the observations are inherently fuzzy, e.g., if the observations are described by linguistic terms [4,5,6] In such cases, the deviations are not due to randomness, but they are due to fuzziness and fuzzy regression should be used. The fuzzy regression is an efficient alternative to statistical regression whenever a dataset is insufficient to support statistical regression analysis [7]
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