Random generation of k-interactive capacities

The theory of capacities provides powerful formal methodology to account for criteria dependencies in multiple criteria decision problems. The discrete Choquet and Sugeno integrals aggregate criteria valuations accounting for criteria synergies and redundancies. We address an important problem of randomly generating capacities of special classes for simulation studies and for capacity learning through evolutionary algorithms. We discuss two efficient methods suitable for k-interactive capacities. The results are supported by the extensive numerical evidence and provide a useful tool for large scale simulations.