Fuzzy测度空间上的泛积分

The Pan-intagrai on the Fuzzy Measure Space

本文利用R_+=〔0,∞〕上的两种二元运算给出了Fuzzy测度空间上非负可测实函数泛积分的定义,证明了泛积分的一些性质,讨论了泛积分序列的几个收敛定理,并论证了〔1〕,〔3〕,〔4〕中有关积分的定义均可作为泛积分之特殊情形。

In this paper, We establish the definition of pan-integral of a nonncgative measurable function on a fuzzy measure space by using two binary operations. Some properties of pan-integral are discussed. Several convergence theorems of pan-integral sequences are also given. Furthermore, we show that the definition of fuzzy integral in[1]and[3], and the definition of Lebosgue integral in[4]are the Special cases of pan-integral.