Some aspects of non-additive measures

It is a well known fact that non-additive measures, i.e., monotone set functions, and corresponding integrals have been successfully applied in many different areas, both theoretical and practical. Due to the course of research, this problem has diversified into two directions. One direction covers real-valued set functions, while the second one leads towards the set-valued case. The first option can be considered as the more classical one and it covers some well known notions, such as the Choquet integral, the Sugeno integral, etc. On the other hand, the set-valued form has imposed itself as being worth studying since, while working with uncertainty, instead of the actual values, sets (intervals) are quite often being used. Lately, decision making theory has emerged as the area of special interest in terms of research of possible applications of non-additive measures. The benefits of the use of non-additive measures and corresponding integrals lie in the flexibility that is provided precisely by the monotonicity of non-additive measures and which is essential for modelling the Decision Maker's behavior. Therefore, the focus of this presentation is on some interesting aspects of non-additive measures and decision making theory.