Linear Model With Exact Inputs and Interval-Valued Fuzzy Outputs

This paper considers the classical semiparametric partially linear model with exact inputs and interval-valued fuzzy outputs. For this purpose, the most commonly used classical two-phase procedure is extended to estimate an interval-valued fuzzy smooth function using nonparametric kernel methods at phase 1 and a least absolute deviation method at phase 2 to estimate the interval-valued fuzzy coefficients. A potential application of the proposed method is presented by a simulated data in hydrology study and an applied example. The proposed interval-valued semiparametric partially linear model is also examined to compare with the interval-valued fuzzy linear regression model via some extended goodness-of-fit criteria into the space of interval-valued fuzzy numbers.