Bipolarity and Multipolarity in Aggregation Structures

In recent years, there has been an increasing interest in handling (heterogeneous) bipolarity in order to deal more adequately with user preferences in information management. Different approaches have been presented. With respect to criteria specification in either flexible database querying or decision support, a main distinction can be made between bipolarity that is specified inside a single criterion and bipolarity that is specified among multiple criteria. Consider criteria that are defined over the values of a given domain. With bipolarity inside a criterion specification, a user might for example state which domain values she likes (positive pole) and which domain values she doesn’t like (negative pole). Herewith, both poles do not have to be the complement of each other. With bipolarity among multiple criteria, in general two poles of criteria are given different semantics and handled in a different way. In this paper we survey different forms of bipolarity among multiple criteria from the standpoint of aggregation and try to classify them into two groups: bipolarity based on positive (desirable) and negative (undesirable) criteria and bipolarity based on nonuniform inputdependent annihilators. Moreover, we present canonical forms of aggregators of the two groups.