Integration defined with respect to a capacity allows for aggregation to be performed in a way that accounts for interaction between variables. The Choquet and Sugeno integrals are two such examples of what are often referred to as “fuzzy integrals”, with their behaviour as aggregation functions understood from the properties of the underlying capacity and related value and interaction indices. This chapter gives an overview of these functions, including some alternative expressions and practical steps for calculation.

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Fuzzy Integrals

  • Gleb Beliakov,
  • Simon James,
  • Jianzhang Wu

摘要

Integration defined with respect to a capacity allows for aggregation to be performed in a way that accounts for interaction between variables. The Choquet and Sugeno integrals are two such examples of what are often referred to as “fuzzy integrals”, with their behaviour as aggregation functions understood from the properties of the underlying capacity and related value and interaction indices. This chapter gives an overview of these functions, including some alternative expressions and practical steps for calculation.