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Fuzzy and probabilistic interpretation of spectral information

The paper shows on a spectroscopical example, how expert knowledge can be modeled by fuzzy sets or in the probabilistic sense as conditional density functions. Fuzzy sets, so-called fuzzy observations, are used to model the information available about frequency positions of main vibrations. These vibrations appear in infrared or RAMAN spectra as absorption bands. The calculation of such vibrations by means of normal coordinate analyses (NCA) often leads to a fitting of calculated frequency positions to experimental ones. Fuzzy methods can be used to evaluate calculated eigenfrequencies in the light of fuzzy observations. In the probability sense, this evaluation can be managed by Bayesian methods. Finally, comparing the fuzzy and probability approach, we conclude that both methods lead to comparable formulas and results.