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

• Published in: IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028) Vol. 3; pp. 79 - 83 vol.3
• Main Authors: Kato, Y., Okamoto, H., Ohtsuki, R., Yamaguchi, S.
• Format: Conference Proceeding
• Language: English; Japanese
• Published: IEEE 20.01.2003
• Subjects: Earth; Extraterrestrial measurements; Fuzzy set theory; Fuzzy sets; Humans; Probability distribution; Random variables; Uncertainty
• ISBN: 9780780357310; 0780357310
• ISSN: 1062-922X
• DOI: 10.1109/ICSMC.1999.823158

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.