Bipolarity and Multipolarity in Aggregation Structures

摘要

Naturally dealing with information processing tasks such as database querying, information retrieval, and decision support requires the adequate handling of bipolarity that might be present in the specification of user preferences in selection criteria. Indeed, past and recent research revealed that users often express their preferences for criteria specifications in a bipolar and sometimes even multipolar way. This means, among others, that different poles of criteria are distinguished, each of them having different semantics and being handled in a different way. For example, a pole of positive (desirable) criteria and a pole of negative (undesirable) criteria might be distinguished. Positive criteria express what the user wants, e.g., a black or blue car, whereas negative criteria express what the user does not want, e.g., a pink car. Likewise, a pole of mandatory criteria, which all have to be satisfied, and a pole of optional criteria, whose satisfaction or dissatisfaction might, respectively, result in a bonus or penalty, can be considered. In this chapter, we study and discuss different manifestations of bipolar and multipolar poles of criteria expressing user preferences from the standpoint of aggregation and try to classify them into two groups: bipolarity based on positive (desirable) and negative (undesirable) poles and bipolarity based on nonuniform input-dependent annihilators. For both groups, we propose canonical forms of aggregators which allow to aggregate criteria evaluations consistently with human reasoning. Moreover, we study how combinations of different forms of bipolarity can lead to multipolarity in criteria specifications and how aggregators for multipolar criteria evaluations can be constructed. This chapter is an extended and revised version of our contribution entitled 'Bipolarity and Multipolarity in Aggregation Structure' to the 4th World Conference on Soft Computing, May 25-27, 2014, UC Berkeley, CA, USA.