A question regarding fuzzy measures


Subject: A question regarding fuzzy measures
From: Goldberg Felix (sgefelix@techst02.technion.ac.il)
Date: Thu Jan 27 2000 - 19:35:09 MET


Dear ladies and gentlemen,
I have a very basic question about fuzzy measures, as I am very new to
the field:
I understand that fuzzy sets serve for modeling vagueness while fuzzy
measures serve for modeling ambiguity. But, if a fuzzy measure is a
function that maps a set of crisp sets to [0,1], then can't a fuzzy
measure be represented as a fuzzy set as well? I mean, can we consider
a fuzzy measure as an assignment of membership grades in some
"super-fuzzy" set to the crisp sets (i.e. the subsets of the universe of
discourse). In that case, if my reasoning is correct, the difference
between vagueness and ambiguity becomes slightly vague, or, perhaps,
ambiguous.
I would be extremely grateful, if somebody could explain the matter to
me.

Thanks in advance,
Felix Goldberg.

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