An improvement to generalized regret based decision making method considering unreasonable alternatives

Regret decision theory is a classic theory for decision problem. Recently, Yager proposed a generalized regret based decision-making method, which calculates the effective regret associated with an alternative by aggregating this alternative's all regrets across all the possible states of nature. The generalized regret based decision-making method that can be applied in many fields is understandable and effective. However, as Yager pointed, an issue limits the application of this method, that is, the generalized regret based decision-making method is lack of indifference to irrelevant alternatives. In this paper, we analyze the cause of this issue, that is, unreasonable alternatives may change other alternatives' regrets by changing the maximal payoff under the occurrence of a state of nature. Furthermore, a new method based on original model is proposed to reduce the impact of unreasonable alternatives according to a parameter called impact factor defined to measure an alternative's quality. Finally, several numerical examples are illustrated to show this new method's effectiveness.