Decomposable and k-additive multi-capacities and multi-polar capacities

Extensions of several concepts for definition of capacities given by a small number of parameters in the unipolar and bipolar framework to the case of multi-polar input spaces are studied. The paper covers decomposable, symmetric, category symmetric, additive, reduced additive and k-additive multi-(polar) capacities and discusses its properties. The multi-polar Möbius transform of multi-polar capacities is introduced and its properties for coordinate-wisely given, additive and k-additive multi-polar capacities are described.