Decision-making under uncertainty
Decision making under uncertainty is the process of choosing the best option when complete information about the external environment, potential consequences, and the probabilities of events is unavailable. In such situations, the decision maker (DM) cannot quantitatively describe or predict the probabilities of states that affect the outcome and must act based on incomplete, inaccurate, or qualitative information.
Sources of Uncertainty
Uncertainty in decision-making problems can arise from various sources:
- Conflict (active) uncertainty — arises from the presence of other participants pursuing their own goals, making their behavior unpredictable. Such situations are modeled using game theory.
- Passive uncertainty (games against nature) — results from a lack of knowledge about objective external conditions (states of nature) that are not influenced by the DM's will. These situations are described within the framework of statistical decision theory and are often called games against nature.
- Semantic (fuzzy) uncertainty — is caused by the inability to clearly describe the situation, alternatives, and preferences in natural language. This includes verbal assessments, qualitative parameters, and unstructured judgments. These problems are studied using fuzzy logic and fuzzy set theory.
- Informational uncertainty — stems from incomplete, inaccurate, or noisy data (e.g., measurement errors, subjective assessments, lack of statistics).
Approaches to Reducing Uncertainty
Uncertainty can be partially eliminated or reduced by:
- obtaining additional information (through observation, expert consultation, testing);
- moving to probabilistic assessment (if statistical analysis is possible);
- using fuzzy models when information is qualitative or verbal in nature;
- structuring the problem (e.g., by creating a decision tree or developing scenarios).
Classical Criteria for Decision Making under Uncertainty
In a situation of uncertainty, the decision maker (DM) does not know which of the possible states of nature will occur. To make a choice, special approaches called criteria are used, each reflecting a particular mindset, level of caution, or attitude toward risk.
- Wald's criterion (cautious choice). This criterion is for those who seek to minimize potential losses. The DM assumes that the most unfavorable outcome will occur and, from all alternatives, chooses the one that provides the best possible result in the worst-case scenario. In other words, it is an approach of maximum caution: "I will choose what is guaranteed to cause the least damage, even if everything goes wrong."
- Suitable for: high-risk situations, critical decisions where failure is not an option.
- Savage's criterion (minimax regret). This approach is focused on avoiding the feeling of regret after discovering that a different choice would have been more beneficial. The DM assesses how much they could lose by making the wrong choice and selects the alternative for which the maximum regret is the smallest.
- Suitable for: individuals prone to self-reflection and the fear of "missing a better opportunity," as well as in competitive environments.
- Laplace's criterion (equal probability). The DM assumes that all possible states of nature are equally likely, as there is no reason to believe otherwise. They then choose the alternative that yields the best average outcome.
- Suitable for: situations with complete symmetry of ignorance, where all outcomes are considered equally possible, and there are no preferences.
- Hurwicz's criterion (compromise). This is a balanced approach that combines caution with a desire for the best outcome. The DM pre-defines their level of optimism (as a coefficient) and chooses the alternative that provides the best combination of possible and guaranteed results based on this attitude.
- Suitable for: situations where a balance between security and profit is important, and there is a personal attitude toward risk.