Fig. 1. Illustration of fuzzy linear regression algorithm and degree of fitting of _i to given fuzzy observation _i. The upper panel indicates how the upper and lower bounds are constructed with a degree of belief (H); A₀ is the intercept and A₁ is the slope of the linear relationship between X and Y; m₀ and m₁ are the center of the fuzzy number A₀ and A₁. c₀ and c₁ are the half width of the fuzzy number A₀ and A₁. The lower panel illustrates how the fuzzy linear regression was constructed. c_j·|X_j| is the zero-cut distance from the center and (1 – H)c_j·|X_j| is the H-cut distance from the center. Since m₀ + m₁·X is the center line, m₀ + m₁·X ± c_j·|X_j| are the 0-cut upper and lower boundaries and m₀ + m₁·X ± (1 – H)c_j·|X_j| is the H-cut upper and lower boundaries. Fuzzy linear regression is to minimize the total fuzziness criterion (Eq. [5]), with constraints that all measurements falls between the H-cut upper and lower boundaries.