The probability measure for a fuzzy event in a fuzzy sample space-a study based on the principle of complete ignorance

Proposes an idea for the problem of how to rationally qualify the probability measure for a vague event in a vague sample space after a subject considers the event and the sample space, and clarifies the vagueness by use of his subjective judgment and fuzzy sets theory. The following points are studied: (1) the probability measure is calculated by use of the principle of complete ignorance and expressed as the measure with possibility; (2) the fuzzy random variable is defined and its possible and necessary probability distributions are derived from studies in Zadeh (1978); (3) the Bayes estimation method based on vague observation is studied; and (4) the consideration of the probability measure studied in the above paper is given based on the possibility/probability consistency principle