A decomposition of additive set functions

Σ-null-additive Set Functions

There is introduced the notion of σ-null-additive set function as a generalization of the classical measure. There are proved the relations to disjoint and chain variations. The general Lebesgue decomposition theorem is obtained. AMS Mathematics Subject Classification (2000): 28A25

A Decomposition for Complete Normed Abelian Groups with Applications to Spaces of Additive Set Functions

Additive Set Functions as Linear Functionals

We discuss the connection of additive set functions to dual function spaces by means of integrals. Isometrical isomorphisms are presented between: a) bounded contents and the dual of uniformly approximable functions, b) charges on Baire algebras and the duals of bounded, continuous functions over A-topological spaces, c) Hewitt measures on Baire σ-algebras and the duals of continuous functions ...

Interactive Multiobjective Optimization Using a Set of Additive Value Functions

In this chapter, we present a new interactive procedure for multiobjective optimization, which is based on the use of a set of value functions as a preference model built by an ordinal regression method. The procedure is composed of two alternating stages. In the first stage, a representative sample of solutions from the Pareto optimal set (or from its approximation) is generated. In the second...

Multiple criteria sorting with a set of additive value functions

We present a new multiple criteria sorting method that aims at assigning actions evaluated on multiple criteria to p pre-defined ordered classes. The preference information supplied by the decision maker (DM) is a set of assignment examples concerning reference actions. Each assignment example specifies a desired assignment for a reference action to one or several contiguous classes. The assign...