Q-expected utility of p-approximated generalized lotteries of I type using Wald, maximax and Hurwiczα criteria
journal contribution
posted on 2023-05-20, 08:32 authored by Nataliya Nikolova, Mednikarov, B, Dimitrakiev, D, Kiril TenekedjievKiril TenekedjievOur focus is on one-dimensional fuzzy-rational generalized lotteries of I type, where the set of prizes is continuous, and the uncertainty is partially quantified 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 modifications 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 Hurwiczα. 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 Hurwiczα expected utility to rank them. We prove that to find 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 find the Wald-expected utility of a one-dimensional p-fuzzy-rational generalized lottery of I type is proposed, along with six simplified algorithms analyzing the cases when the utility function is either partially linearly interpolated or arctan approximated and also interprets different types of preferences (monotonic or non-monotonic). The maximax and Hurwiczα expected utilities are then derived using trivial modifi cations of the procedures developed for the Wald expected utility. Two numerical examples demonstrate the application of the procedures.
History
Publication title
Information Technologies and ControlPagination
2-17ISSN
1312-2622Department/School
Australian Maritime CollegePublisher
SciendoPlace of publication
PolandRepository Status
- Restricted
