Fuzzy measure question

Holger Hebben (hebben@clio.rz.uni-duesseldorf.de)
Mon, 18 Dec 1995 19:58:40 +0100

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I got the following problem:
In the book FUZZY SETS AND THEIR APPLICATIONS TO COGNITIVE AND
DECISION PROCESSES edited by Zadeh et. al. the contribution of
T. Terano and M. Sugeno: CONDITIONAL FUZZY MEASURES AND THEIR
APLLICATIONS (pages 151 - 170) introduces a fuzzy measure g
(definition 1 p. 153) and a fuzzy integral in formula (2.1)
(p. 154) After giving some properties in formulas (2.2) to (2.8)
they define in (2.9) again a fuzzy measure (of a fuzzy set A)
by equating g(A) with the fuzzy integral of the membership
function of A with respect to a fuzzy measure g, i do not see
how this definition works, as g appears on both sides.
In formula (2.10) they again define a fuzzy integral (over A):
The left side of (2.10) is the same as in (2.1), but i can not
see that the right sides are in general the same.
Anything that clears the darkness in my brain is very welcome!
One last question: What is the state of the art right now?
Where can i find literature about fuzzy measurement and integration?

Thanx in advance

Holger

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