This is subsequent of , by using the theory of additive fuzzy measure and signed additive fuzzy measure , we prove the Radon_Nikodym Theorem and Lebesgue decomposition Theorem of signed additive fuzzy measure.
In this paper, we introduce the concept of signed additive fuzzy measure on a class of fuzzy sets, then, on certain condition, a series of decomposition theorems of signed additive fuzzy measure are proved.
The relations among three kinds of structural characteristics of fuzzy measure: (1) pseudometric generating property; (2) pseudometric generating property of type p; (3) null null additivity, and the convergence for ...The relations among three kinds of structural characteristics of fuzzy measure: (1) pseudometric generating property; (2) pseudometric generating property of type p; (3) null null additivity, and the convergence for sequence of measurable function on semi continuous fuzzy measure space are discussed. A set of equivalent conditions for each of these structural characteristics are presented, respectively. It is proved that null null additivity is equivalent to pseudometric generating property for a finite fuzzy measure on S compact space.展开更多
The concept of fuzzy measure was introduced by Sugeno in 1974. A notion of signed fuzzy measure is introduced in this paper, and its elementary properties are briefly discussed. An analogue of Hahn decomposition theo...The concept of fuzzy measure was introduced by Sugeno in 1974. A notion of signed fuzzy measure is introduced in this paper, and its elementary properties are briefly discussed. An analogue of Hahn decomposition theorem is established under the null-null-additive condition. A version of the Jordan decomposition theorem is proved under the null-additive condition.展开更多
文摘This is subsequent of , by using the theory of additive fuzzy measure and signed additive fuzzy measure , we prove the Radon_Nikodym Theorem and Lebesgue decomposition Theorem of signed additive fuzzy measure.
文摘In this paper, we introduce the concept of signed additive fuzzy measure on a class of fuzzy sets, then, on certain condition, a series of decomposition theorems of signed additive fuzzy measure are proved.
文摘The relations among three kinds of structural characteristics of fuzzy measure: (1) pseudometric generating property; (2) pseudometric generating property of type p; (3) null null additivity, and the convergence for sequence of measurable function on semi continuous fuzzy measure space are discussed. A set of equivalent conditions for each of these structural characteristics are presented, respectively. It is proved that null null additivity is equivalent to pseudometric generating property for a finite fuzzy measure on S compact space.
基金Supported by the National Natural Science Foundationof China( Nos. 6 0 2 740 5 0 and70 1710 36 )
文摘The concept of fuzzy measure was introduced by Sugeno in 1974. A notion of signed fuzzy measure is introduced in this paper, and its elementary properties are briefly discussed. An analogue of Hahn decomposition theorem is established under the null-null-additive condition. A version of the Jordan decomposition theorem is proved under the null-additive condition.
