An algorithm for fuzzy linear calibration

A New Fuzzy Regression Algorithm

“…In the method FUZR by Otto and Bandemer, a circle acts as the support of the fuzzy observations. Relative to the method FUZL by Massart et al, as support of the fuzzy observations, a line appeared to be more suitable.…”

“…It was compared with conventional ordinary and weighted least-squares and robust regression methods. The application of these different methods to relevant data sets proved that the performance of the procedure described in this paper exceeds that of the ordinary least-squares method and equals and often exceeds that of weighted or robust methods, including the two fuzzy methods proposed in refs and .…”

“…Because the weakness of the least-squares method lies in its overemphasis on large values of residuals, these should be deemphasized (downweighted) or perhaps even ignored. For intermediate values of the residuals, the procedure should connect the treatments of the small residuals and the extreme residuals in a smooth or fuzzy fashion. − …”

Treatment of Model Error in Calibration by Robust and Fuzzy Procedures

“…** The stop criterion was fulfilled when more than half of the measurements had a membership value of 0.1 (= H) or more. 3 We carried out fuzzy linear calibration for three selected data sets investigated by them: those for data sets 2, 5 and 8. These were of interest because they were measured with gross outlier, no outliers and with model error, respectively.…”