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.
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.
Let k, m, n be positive integers, and k≥2, α∈(0,1], 0<r<min{m,n} an integer, d=r+(m?r)/(k+α), and if f∈Ck (Rm, ...Let k, m, n be positive integers, and k≥2, α∈(0,1], 0<r<min{m,n} an integer, d=r+(m?r)/(k+α), and if f∈Ck (Rm, ,α Rn), A=Cr(f)={x∈Rm |rank(Df(x))≤r}, then f(A) is d-null. Thus the statement posed by Arthur Sard in 1965 can be completely solved when k≥2.展开更多
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.
基金Project supported by the National Natural Science Foundation ofChina (No. 10171090) and the Scientific Research Fund of ZhejiangProvincial Education Department (No. 20030341) China
文摘Let k, m, n be positive integers, and k≥2, α∈(0,1], 0<r<min{m,n} an integer, d=r+(m?r)/(k+α), and if f∈Ck (Rm, ,α Rn), A=Cr(f)={x∈Rm |rank(Df(x))≤r}, then f(A) is d-null. Thus the statement posed by Arthur Sard in 1965 can be completely solved when k≥2.
