Aggregation Operators

Abstract

Aggregation refers to the process of combining values into a single value so that the final result of aggregation takes into account in a given form all the individual aggregated values. This chapter serves as a theoretical background for applications mainly in the area of decision analysis, decision making or decision support. In decision making, values to be aggregated are typically preference or satisfaction degrees. A preference degree, e.g., v(A, B) tells to what extent an alternative A is preferred to an alternative B. This way, however, will not be followed here. In this chapter the values are understood and interpreted as satisfaction degrees which express to what extent a given alternative is satisfactory with respect to a given criterion — a given real-valued function, or as a kind of distance to a prototype which may represent the ideal alternative for the decision maker. Depending on concrete applications, values to be aggregated can be also interpreted as confidence degrees in the fact that a given alternative is true, or as expert’s opinions, similarity degrees, etc., see, e.g., [29].