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
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.
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.
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.
