Aggregation in Interval-Valued Settings

Aggregation functions for interval-valued fuzzy settings derive from the concept of an aggregation function defined on the unit interval [0, 1]. This is why we begin with recalling the most important properties of aggregation functions as well as a short historical development of this concept. Next, classes, properties and construction methods of aggregation functions defined for interval-valued settings are provided. We pay special attention to the new classes of aggregation operators, namely possible and necessary aggregation functions. We present examples, properties, construction methods and dependencies between these two classes of operators and other well-known aggregation operators applied in interval-valued fuzzy settings. The presented results may be also useful for the entire community, not only fuzzy, involved in research under uncertainty or imperfect information.