Fuzzy ranking and quadratic fuzzy regression

Three different ranking methods, namely, the overall existence ranking index (OERI), the approach proposed by Diamond [1] and a new two-step method based on OERI, are used to estimate the distance between two fuzzy numbers. This distance parameter is then used in the least square or quadratic regression. Nonlinear programming is used to solve the resulting quadratic regression equations with constraints, and simulation is used to evaluate the performance of the approaches. The criterion used to evaluate the performance is the average of the absolute difference between the estimated and the observed values. It appears that the two-step OERI obtains better results for the case of small sample size and Diamondʹs approach gets better as the sample size increases.