INSTITUTE OF INFORMATION TECHNOLOGIES - BAS
Cybernetics and Information Technologies
Volume 6, No 3. Sofia, 2006, Bulgarian Academy of Sciences
Laplace Expected Utility Criterion for Ranking Fuzzy Rational Generalized Lotteries of I Type
Kiril Tenekedjiev, Natalia Nikolova, Daniela Toneva
Technical University, 9010 Varna,
E-mails: kiril@dilogos.com, natalia@dilogos.com, eley_simeonova@abv.bg
Abstract:
Real decision makers partially disobey axioms of rationality and are called fuzzy rational. Fuzzy rationality in probabilities leads to the construction of x-ribbon and p-ribbon distribution functions, whose quantiles/quantile indices are elicited as uncertainty intervals. As a result x-fuzzy rational and p-fuzzy rational generalized lotteries are introduced and a general approach to rank each type is developed, which approximates ribbon functions by classical partially linear ones and then applies expected utility. In this paper, approximation is made via Laplace criterion under strict uncertainty. Its use is formalized for both types of ribbon functions. Laplace expected utility is also introduced to rank p-fuzzy-rational and x-fuzzy-rational generalized lotteries of I type. An example is developed to show the importance of decision modeling and detailed analysis of available subjective information for the final decision.
Keywords:
fuzzy rationality, subjective probability, strict uncertainty, generalized lotteries, ribbon functions, expected utility, Laplace strict uncertainty criterion.