Fuzziness and loss of information in statistical problems

Statistical problems in which the available experimental observations are not necessarily exact have been described previously by means of a probabilistic-possibilistic approach based on the concept of the fuzzy information system. When Zadeh´s probabilistic definition (1978) is adopted, the gain of information about the state of nature or parameter contained in a fuzzy information system and the uncertainty associated with an inference from it could be quantified in this approach by means of several concepts. The author proves that the fuzziness in the experimental observations entails a loss of information about the state or parameter space, whatever the quantification of the gain of information or the uncertainty may be.