The following is a post I published elsewhere in a previous version of my blog, on 28 March 2009.
Dear Professor Zadeh,
This piece is intended as a comment on recent posts about probability theory to the BISC mailing list, in reaction to your initial post of 18 March 2009, called `What is probability?’. You clarified and revised the text a bit in your message of 25 March 2009.
You and I have argued, both in private and in public, about the issues raised there a few times before. Since I have never really summed up my point of view to you, I thought this might be a good opportunity.
If I try to reduce what you say in your message to its bare essentials, I come up with the following:
Consider (some person’s assessment of) the probability of an event. Then, first of all, this probability need not be a precise number, and we need a theory to deal with this. And, secondly, probability theory has always considered events to belong to the realm of two-valued logic: they either occur or they don’t, tertium non datur. And, so you argue, we need to be able to deal with what you call fuzzy events, which may occur to some degree.
The work that many people, including me, have been doing in what I shall call Imprecise Probabilities for want of a commonly accepted name (see Peter Walley’s book  for a good starting point, SIPTA may also be of interest) is related to the first observation: probability need not be a precise number. I shall try and deal with this first, before turning to your second point, probabilities of fuzzy events.