BOUML DIRECTION AGGREGATION FULL

In this paper, we propose to abandon the current order-based understanding of an aggregation process and embrace a new geometrically-oriented sense upon which a new theory of aggregation could be developed. Some prominent examples are the aggregation of strings, which is nowadays a popular topic for computer scientists and bioinformaticians, and the aggregation of rankings, which has been studied in social choice theory since the eighteenth century. Although the most popular aggregation processes have historically been those dealing with real numbers, the interest of practitioners in different types of data is not to be neglected. For instance, means were already studied by Cauchy in the early 1820s. Although the field in itself only dates from the second half of the last century, one could easily trace back further in time prominent examples of aggregation functions. The field of aggregation theory aims at formalizing in a mathematical way the process of combining several inputs into a single output, typically both the inputs and the output being elements of a poset. Therefore a new class of operators is suggested which varies with respect to a parameter of compensation. However, they do not predict our data very well. The results of our experiments support the hypothesis that people often use compensatory procedures. This indicates that human beings partially are using non-verbal aggregation procedures which do not correspond to the verbal and logical connectives ‘and’ and ‘or’. The aggregation of subjective categories in the framework of human decisions or evaluations almost always shows some degree of compensation.

BOUML DIRECTION AGGREGATION FULL

If, on the other hand, a decision is defined to be the union of fuzzy sets, represented by the maximum or algebraic sum of the degrees of membership, full compensation is assumed.Managerial decisions hardly even represent any of these extremes. The interpretation of a decision as the intersection of fuzzy sets, computed by applying either the minimum or the product operator to the membership functions of the fuzzy sets concerned implies that there is no compensation between low and high degrees of membership.

Bouml direction aggregation