Fuzzy Prediction in Regression

Abstract

From the previous chapter we have our fuzzy regression equation

$$\overline y \left( {\mathop x\nolimits_1 ,\mathop x\nolimits_2 } \right) = \overline a + \overline b \mathop x\nolimits_1 + \overline c \mathop x\nolimits_2 $$

(26.1)

for $\bar{y}$(x ₁, x ₂), with ā, $\bar{b}$ and $\bar{c}$ fuzzy numbers and x ₁, x ₂ real numbers. $\bar{y}\,=\,({{x}_{1}},{{x}_{2}})$ is our fuzzy number estimator for the mean of Y (E(Y)) given xi and x ₂, and we show this dependence on x ₁ and x ₂ with the notation $\bar{y}\,=\,({{x}_{1}},{{x}_{2}})$. We may choose new values for x ₁ and x ₂ to predict new fuzzy values for E(Y).