Derived Fuzzy Measures and Derived Choquet Integrals With Some Properties

The well-known Choquet integrals are based on given fuzzy measures, providing some sound schemes for the evaluation problems in multicriteria decision making. To further generalize and diversify these interesting aggregation functions, this article proposes the concept of derived fuzzy measures, which can serve as a generalization of normally used fuzzy measures. Based on derived fuzzy measures, we present the detailed integral methods to define the corresponding derived Choquet integrals. With some specific derived fuzzy measures, we find that both Choquet and Sugeno integrals are special cases of derived Choquet integrals. In addition, some relevant properties and propositions with practical explanations are also discussed, for example, the less/more increment properties and amplifying/attenuating properties.