Propozycja hybrydy reguł Hurwicza i Bayesa w podejmowaniu decyzji w warunkach niepewności

The Hurwicz rule and the Bayes rule are classical approaches applied in the decision making under uncertainty. This situation occurs when the decision maker may choose one of several alternatives and he or she is only able to assign to each of them an interval of potential payoffs or a set of possible profits. In both cases the answer obtained depends on the state of nature (scenario) which will happen, but in the first case the set of scenarios is infinite and in the second one - it is finite. The Hurwicz measure, with the aid of the coefficient of pessimism and the coefficient of optimism, enables to find the optimal pure strategy when the decision selected is performed only once. Meanwhile the Bayes criterion is designed to indicate the optimal pure or mixed strategy when the variant chosen is performed once or many times. In the first part of the article the author analyzes the Hurwicz rule and illustrates cases when the use of this criterion leads to quite unexpected results which seem to be contradictory with the logic and do not reflect the decision maker's preferences. In the second part a proposal of an approach for optimal pure strategy searching (by means of formulas considering both the coefficients of pessimism and optimism, as well as the whole set of payoffs) is presented. This procedure (H+B rule) combines elements of the Hurwicz criterion and the Bayes criterion, but is deprived of disadvantages typical of the Hurwicz rule. The rule suggested takes into consideration both extreme payoffs and intermediate payoffs, which enables to receive rational recommendations for a larger spectrum of decision problems. The H+B rule may be applied in the decision making process under uncertainty when the number of potential scenarios and the set of possible payoffs are finite, however a slight modification of the equations proposed enables to use this procedure in problems with continuous payoffs.