Lotfi A. Zadeh wrote:
> The problem is: probability theory does not differentiate between
> fuzziness and randomness or, concomitantly, between possibility and
> probability. Here is a simple example. I meet Valentina. I do not know
> how old she is. My perception is that she is about 40. In this instance,
> Valentina's age is a fuzzy variable and "about 40: is its fuzzy value.
Lotfi's case is very important, as it demonstrates the difference
between the value of a random variable and a distribution over a random
variable. Let me rephrase the above example in probabilistic terms:
I meet Valentina.
I observe the values of several variables {Skin="slight wrinkles",
Hairstyle="Formal", Dress="Skirt_Blouse"}
I do not know how old she is.
I do not know the value of variable Age. Having previously observed
similar women and men and knowing their ages, I could build a
probabilistic model P(Age|Skin,Hairstyle,Dress). Since I have not seen
all the women in the world, and I had started from a subjective prior,
the model is also subjective and Bayesian.
My perception is that she is about 40.
To quickly summarize the P(Age|Skin="slight
wrinkles",Hairstyle="Formal",Dress="Skirt_Blouse"), I can use the mean
of the conditional distribution.
In this instance, Valentina's age is a fuzzy variable and "about 40" is
its fuzzy value.
Valentina's age is a subjective probability distribution, and 40 is the
rounded value of its mean.
Best regards,
Aleks Jakulin
Department of Statistics
Columbia University
_______________________________________________
uai mailing list
uai@ENGR.ORST.EDU
https://secure.engr.oregonstate.edu/mailman/listinfo/uai
