Despite the fuzziness of information, it is often necessary to choose the optimal, most cautious strategy, e.g. in economic planning, in conflict situations, in daily decisions. this is impossible without the concept of fuzzy equilibrium. The concept of fuzzy stability is considered, as an extension into a time interval, taking into account the corresponding stability area of the decision maker. The more complex the model, the more soft a choice has to be considered.

The idea of fuzzy equilibrium is based on the optimization principles. Therefore the MaxEmin-, MaxGmin- and PDP-stability have to be analyzed. The violation of these principles leads often to wrong predictions and decisions.

 

The LPI - equilibrium point

We shall consider a given LPI-decision model, as a convolution of the corresponding fuzzy states - a disturbance set /7/. The fuzzy equilibrium strategy remains the most cautious one, despite of the fuzziness presence. Any deviation from this strategy can cause a loss for the decision maker.