Necessity and sufficiency in aggregation based on non-decreasing functions

Abstract

The paper introduces the concept of aggregation of indicators as a mapping of a set of their values into a single numer-ical value (named aggregate) using a bounded non-decreasing and non-constant function U(X). The concepts of aggre-gation by necessity and sufficiency are introduced and it is shown that there are no other options for such aggregation. The properties of aggregation by necessity and sufficiency are investigated. The concepts of value and utility of a sub-set of indicators as measures of its necessity and sufficiency are introduced. The value is related to the decrease amount of aggregate when minimizing the indicators included in the corresponding subset, and the utility is related to the value of the aggregate when only these indicators take the maximum value. It is noted that the properties of aggre-gated systems (systems for each component of which there is an aggregate) are determined by the laws of aggregation among other things. For example, that each aggregated system has a core, i.e. a subset of components (subsystems and functional elements), the functionality of which determines the functionality of the system as a whole and this is not due to the nature of the system, but only to the fact that it is aggregated.