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Here, we present various transformations and capacity representations, including the Möbius and interaction indices of the previous chapter. While we have seen that these alternative forms can help facilitate interpretation and provide insight into different aspects of a capacity’s composition, the focus of this chapter is on the simplifications and improvements in efficiency that can be obtained from a practical perspective. Vector representation and linear transformation matrices are introduced, which allow for efficient computer implementation, as well as expressions for different indices in marginal contribution representation and an overview on the polytope of normalised capacities.

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Representations

  • 章节

  • 发表日期：

    2026年

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  • Gleb Beliakov,
  • Simon James,
  • Jianzhang Wu

摘要

Here, we present various transformations and capacity representations, including the Möbius and interaction indices of the previous chapter. While we have seen that these alternative forms can help facilitate interpretation and provide insight into different aspects of a capacity’s composition, the focus of this chapter is on the simplifications and improvements in efficiency that can be obtained from a practical perspective. Vector representation and linear transformation matrices are introduced, which allow for efficient computer implementation, as well as expressions for different indices in marginal contribution representation and an overview on the polytope of normalised capacities.