Fuzzy Linear Regression Method in Ultratrace Analysis and Analytical Interpretation

Fuzzy sets theory was introduced for quantitative treatment of measured values in ultratrace analysis. The data obtained in extremely low concentration have uncertainties such as errors of measurement or errors arising from chemical handling of the samples. In place of the least squares method, a fuzzy linear regression method was applied to measured values expressed by the fuzzy numbers, and instead of a calibration curve, a calibration area was obtained. The validity and propriety of the calibration area were shown from simulation and experimental data of ultratrace analyses done using laser induced photothermal spectrometry. Analytical meanings of the shape of the calibration area were discussed.