Since the appearance of the first paper on fuzzy sets proposed by
Zadeh in 1965, the relationship between probability and fuzziness in the representation
of uncertainty has been discussed among many people. The question is
whether probability theory itself is sufficient to deal with uncertainty. In this paper
the relationship between probability and fuzziness is analyzed by the process of
perception to simply understand the relationship between them. It is clear that
probability and fuzziness work in different areas of uncertainty. Here, fuzzy event
in the presence of probability theory provides probability of fuzzy event in which
fuzzy event could be regarded as a generalization of crisp event. Moreover, in
rough set theory, a rough event is proposed representing two approximate events,
namely lower approximate event and upper approximate event. Similarly, in the
presence of probability theory, rough event can be extended to be probability of
rough event. Finally, the paper shows and discusses relation among lower-upper
approximate probability (probability of rough events), belief-plausibility measures
(evidence theory), classical probability measures, probability of generalized
fuzzy-rough events and probability of fuzzy events
