Fuzzy expected value

Subject: Fuzzy expected value
From: Chongfu Huang (hchongfu@yahoo.com)
Date: Sat Jun 10 2000 - 07:30:08 MET DST

Dear Gerhard Moeller,

I am sorry it may take some time for you to help me
in fuzzy expected value.

According to the material from your email dated
Sun, 16 Apr 1995 (http://www.dbai.tuwien.ac.at/
marchives/fuzzy-mail95/0460.html), you are
interested in the topic, and you might read some

Now, I am studying the risk management of natural
disasters involving complex systems. We cannot
get probability-risk, but only some fuzzy probability.
In our case, the probability value of a crisp event
is a fuzzy number, the probability density function
is a 2-dimension possibility distribution defined on
probability
space and events space. I have to calculate its
expected value.

[1] Pal, S.K.(1986), Fuzzy Mathematical
Approach to Pattern Recognition. John Wiley, New York.
[2]Zadeh, L.A. (1968), Probability measures of fuzzy
events. Journal of Mathematics Analysis and
Applications
{\bf 23} (1), pp.421-427
[3] Kandel, A. and Byatt, W.J.(1978), Fuzzy sets,
fuzzy
algebra, and fuzzy statistics. Proc. IEEE {\bf
66}(12),
pp.1619-1639
[4]Heilpern, S.(1993), Fuzzy subsets of the space of
probability
measures and expected value of fuzzy variable. Fuzzy
Sets and
Systems {\bf 54}(3), pp.301-309
[5] Romer,. C and Kadel, A.(1995), Statistical tests
for
fuzzy data. Fuzzy Sets and Systems {\bf 72}(1),
pp.1-26
[6] Qiao, Z., Zhang, Y. and Wang, G.Y.(1994),
On fuzzy rendam linear programming. Fuzzy Sets and
Systems {\bf 65}(1), pp.41-49

But, I havenˇ¦t found the model and example I need.
Could you please tell me more references? If you have
internet material related to that, send some to me

Thank you so much for your help.

Sincerely yours
Chongfu Huang
===========================================
Dr. Chongfu Huang
Visiting Scholar
PKI 175E
6001 Dodge Street
Omaha, NE 68182-0296
Tel.:(402)554.2562
Email:hchongfu@yahoo.com
=============================================

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