A decision rule based on goal programming and one-stage models for uncertain multi-criteria mixed decision making and games against nature

This paper is concerned with games against nature and multi-criteria decision making under uncertainty along with scenario planning. We focus on decision problems where a deterministic evaluation of criteria is not possible. The procedure we propose is based on weighted goal programming and may be applied when seeking a mixed strategy. A mixed strategy allows the decision maker to select and perform a weighted combination of several accessible alternatives. The new method takes into consideration the decision maker’s preference structure (importance of particular goals) and nature (pessimistic, moderate or optimistic attitude towards a given problem). It is designed for one-shot decisions made under uncertainty with unknown probabilities (frequencies), i.e for decision making under complete uncertainty or decision making under strategic uncertainty. The procedure refers to one-stage models, i.e. models considering combinations of scenarios and criteria (scenario-criterion pairs) as distinct meta-attributes, which means that the novel approach can be used in the case of totally independent payoff matrices for particular targets. The algorithm does not require any information about frequencies, which is especially desirable for new decision problems. It can be successfully applied by passive decision makers, as only criteria weights and the coefficient of optimism have to be declared.