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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. 
cj·|Xj|
is the zero-cut distance from the center and (1 – H)cj·|Xj| is the H-cut distance from the center. Since m0 + m1·X is the center line, m0 + m1·X ± cj·|Xj| are the 0-cut upper and lower boundaries and m0 + m1·X ± (1 – H)cj·|Xj| 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.
