Modifications of the Hurwicz’s decision rule

Abstract

The Hurwicz's criterion is one of the classical decision rules applied in decision making under uncertainty as a tool enabling to find an optimal pure strategy both for interval and scenarios uncertainty. The interval uncertainty occurs when the decision maker knows the range of payoffs for each alternative and all values belonging to this interval are theoretically probable (the distribution of payoffs is continuous). The scenarios uncertainty takes place when the result of a decision depends on the state of nature that will finally occur and the number of possible states of nature is known and limited (the distribution of payoffs is discrete). In some specific cases the use of the Hurwicz's criterion in the scenarios uncertainty may lead to quite illogical and unexpected results. Therefore, the author presents two new procedures combining the Hurwicz's pessimism-optimism index with the Laplace's approach and using an additional parameter allowing to set an appropriate width for the ranges of relatively good and bad payoffs related to a given decision. The author demonstrates both methods on the basis of an example concerning the choice of an investment project. The methods described may be used in each decision making process within which each alternative (decision, strategy) is characterized by only one criterion (or one synthetic measure).

On two applications of the Omega ratio: max?min and Omega(H+B) / O dwóch zastosowaniach wskaźnika Omega: max?min i Omega(H+B)

“…The literature offers numerous decision rules for DMPI [Guo 2013;Kmietowicz, Pearman 1984;Kofler, Zweifel 1993;Michalska, Pośpiech 2010;, Michalska 2012Weber 1987] and for DMCU [Gaspars 2007;GasparsWieloch 2013;2014a;2014b;2014c;2014d;2014e;2015a;2015b;2015c;2015d;2015e;2016;Hayashi 2008;Hurwicz 1952;Ioan, Ioan 2011;Piasecki 1990;Savage 1961;Wald 1950], but here we only investigate the use of the Ω ratio in these two decision cases.…”

A Decision Rule for Uncertain Multi-Criteria Pure Decision Making and Independent Criteria

“…Conclusions are gathered in the last Section. The paper is a continuation of several articles, where uncertain one-criterion procedures [Gaspars-Wieloch, 2007;2014a;2014c;2015b;2016b] and multi-criteria decision rules [Gaspars-Wieloch, 2014d;2015c;2015d;2017] are investigated.…”

Modifications of the Omega ratio for decision making under uncertainty

“…Thus, we see that the Omega(H+B) ratio recommends different strategies depending on the DM's risk aversion, which is certainly a valuable feature of the new approach. The fact that all outcomes concerning particular decisions have an impact on the suggested solution is also advantageous (compare with [16]). …”

“…The literature also offers various extensions or hybrids of those methods, see e.g. [2,3,4,7,8,9,10,11,12,13,15,16,17,18,19,20,27,36,41,46,53]. Nevertheless, the majority of the extended rules refer to the probability calculus (for instance, expected profit maximization, expected utility maximization, subjective expected utility, maximin expected utility, α-maximin expected utility, restricted Bayes/Hurwicz, prospect theory, cumulative prospect theory, Choquet expected utility), which is rather characteristic of DMUR.…”

“…Such a phenomenon is due to the fact that the Hurwicz criterion takes only extreme payoffs into consideration (transitional values connected with a given decision are ignored). Additionally, the above rule does not examine the frequency of relatively high and low payoffs belonging to the set of all profits assigned to particular alternatives (see [11,13,16]). In the H+B rule, in contradiction to the Hurwicz approach, all outcomes have an influence on the value of the final measure.…”