| Key Words |
Ribbon distributions; interval estimates; lotteries;strict uncertainty; expected utility |
| Abstract |
Our focus is on one-dimensional fuzzy-rational generalized lotteries of I type, where the set of prizes is continuous,
and the uncertainty is partially quantifi ed by p-ribbon distribution
functions (CDFs). The p-ribbon CDFs originate from the interval
estimates of quantiles. Our objective is to rank such alternatives
using several modifi cations of the expected utility rule. Initially, we
transform the p-ribbon functions into classical ones using one of
three decision criteria Q under strict uncertainty – Wald, maximax
and Hurwicz?
. That approximated the p-fuzzy-rational generalized
lotteries of I type into classical pQ-generalized lotteries of I type.
We can then calculate the Wald, maximax and Hurwicz?
expected
utility to rank them. We prove that to fi nd those expected utilities
we need to estimate the inner quantile indices of the CDF in the
pQ-generalized lotteries of I type. A universal algorithm to fi nd
the Wald-expected utility of a one-dimensional p-fuzzy-rational
generalized lottery of I type is proposed, along with six simplifi ed
algorithms analyzing the cases when the utility function is either
partially linearly interpolated or arctan approximate |
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