Decision-making under risk and uncertainty and its application in strategic management

We introduce a new decision-making model that unifies risk and uncertain environments in the same formulation. For doing so, we present the induced probabilistic ordered weighted averaging (IPOWA) operator. It is an aggregation operator that unifies the probability with the OWA operator in the same formulation and considering the degree of importance of each concept in the aggregation. Moreover, it also uses induced aggregation operators that provide a more general representation of the attitudinal character of the decision-maker. We study its applicability and we see that it is very broad because all the previous studies that use the probability or the OWA operator can be revised and extended with this new approach. We briefly analyze some basic applications in statistics such as the implementation of this approach with the variance, the covariance, the Pearson coefficient and in a simple linear regression model. We focus on a multi-person decision-making problem in strategic management. Thus, we are able to construct a new aggregation operator that we call the multi-person IPOWA operator. Its main advantage is that it can deal with the opinion of several persons in the analysis so we can represent the information in a more complete way.