Abstract
In practice, there are cases that observations of objects in a population are fuzzy. It is not desirable for the statistical inference to discard the fuzzy data from fuzzy observations or to ignore the effect of fuzziness by reason of the complexity of the treatment of fuzziness.
In this paper, the fuzzy observation with human vagueness on a probability space is considered. The correction formulae eliminating the effect of fuzziness in orderto estimate actual moments and actual cumulants of a population are given, when the moments and cumulants are calculated from fuzzy data obtained by fuzzy observations. Furthermore, the validity of the corrections is investigated by the simulation and the experiment on fuzzy observations.
