The discussion about the integration of set-valued mapping was made in the strong sense. But, many set-valued mappings are not strong integrablc. So, in this paper, the integration of set-valued mapping in weak sense ...The discussion about the integration of set-valued mapping was made in the strong sense. But, many set-valued mappings are not strong integrablc. So, in this paper, the integration of set-valued mapping in weak sense is defined in Banach space, which is called Pettis-Aumann Integration, and the properties of this integration are discussed. The relationship between strong and weak integration and the convexity theorem are established.展开更多
A novel concept, called nonadditive set-valued measure, is first defined as a monotone and continuous set function. Then the interconnections between nonadditive set-valued measure and the additive set-valued measur...A novel concept, called nonadditive set-valued measure, is first defined as a monotone and continuous set function. Then the interconnections between nonadditive set-valued measure and the additive set-valued measure as well as the fuzzy measure are discussed. Finally, an approach to construct a nonadditive compact set-valued measure is presented via Aumann fuzzy integral.展开更多
文摘The discussion about the integration of set-valued mapping was made in the strong sense. But, many set-valued mappings are not strong integrablc. So, in this paper, the integration of set-valued mapping in weak sense is defined in Banach space, which is called Pettis-Aumann Integration, and the properties of this integration are discussed. The relationship between strong and weak integration and the convexity theorem are established.
基金Supported by the National Natural Science Foundationof China ( No. 6 0 1740 49) and Sino- French JointL aboratory for Research in Com puter Science,Controland Applied Mathem atics ( L IAMA)
文摘A novel concept, called nonadditive set-valued measure, is first defined as a monotone and continuous set function. Then the interconnections between nonadditive set-valued measure and the additive set-valued measure as well as the fuzzy measure are discussed. Finally, an approach to construct a nonadditive compact set-valued measure is presented via Aumann fuzzy integral.
