On Metric Aggregation Functions and Fuzzy Decision-Making

Abstract

[eng] In fuzzy decision-making it is required to aggregate numerical pieces of information that incorporate vagueness and that comes from various sources in order to get a unique numerical value that is incorporated in some decision-making technique and, hence, it allows to select one option between several available. In order to select which alternative is the best one, an ideal profile is defined and the alternative chosen is exactly the one that minimizes the distance to the aforementioned ideal. The Ordered Weighted Averaging (OWA) is an instance of aggregation function which appears to be well-suited to be applied in these type of situations. Concretely, it has been shown to be useful in generating mean distances which are used to evaluate all different strategies and to find the best one according to the interest of the decision-maker. However, in a natural way, the decision process imposes many times that the aggregate information corresponds to an overall distance between alternatives rather than an average distance. In this direction, metric aggregation functions are more useful. In this paper, we introduce a technique to generate this type of functions and we show a few limitations of the OWA for this purpose. Instances of such functions induced by the new technique are provided. Moreover, such examples are used to illustrate the usefulness of this type of functions in fuzzy decision-making. The selection of strategies is compared with those provided by the OWA.