Abstract
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.
Highlights
Decision-making problems are very common in our lifes
It is an aggregation operator that provides a parameterized family of aggregation operators between the minimum and the maximum
We briefly present some basic examples in statistics by using the induced probabilistic ordered weighted averaging (IPOWA) operator in the variance, the covariance, the Pearson coefficient and in a simple linear regression model
Summary
We find different methodologies for decision-making. For example, we can mention multiple criteria decision-making, group decision-making and game theory. In decision-making problems it is very interesting to consider a set of arguments a that depend on a set of states of nature S and a set of alternatives A Decision-making “ex-ante”: when we aggregate the information according to an alternative selected and see the potential results depending on the states of nature that happen in the future. The usual management of a company or a country is conditioned both by “ex-ante” and “ex-post” decisions because both processes represent a usual activity in order to obtain the most efficient decisions All these approaches can be mixed because the decision-making process usually involves several sources of information so it is very common that each part is assessed with different techniques. We believe that we have provided an appropriate general overview according to the objectives of the paper
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