Determine maximin,maximax,minimax regret criterions?

The maximin criterion is a decision-making approach that focuses on minimizing the maximum possible loss. It assumes that the decision-maker is risk-averse and wants to protect themselves from the worst-case scenario. The maximin criterion selects the alternative with the highest minimum payoff.

The maximax criterion, on the other hand, is a decision-making approach that focuses on maximizing the maximum possible gain. It assumes that the decision-maker is risk-seeking and wants to achieve the best possible outcome. The maximax criterion selects the alternative with the highest maximum payoff.

The minimax regret criterion is a decision-making approach that focuses on minimizing the maximum regret. Regret is the difference between the payoff of the best alternative and the payoff of the chosen alternative. The minimax regret criterion selects the alternative that minimizes the maximum regret.

In summary:
- Maximin criterion: Selects the alternative with the highest minimum payoff.
- Maximax criterion: Selects the alternative with the highest maximum payoff.
- Minimax regret criterion: Selects the alternative that minimizes the maximum regret.