【作者】 汪彬；

【导师】 王贵君；

【作者基本信息】 天津师范大学 ， 应用数学， 2010， 硕士

【摘要】 本文共分两个部分.第一部分：首先,在区间值函数的Mcshane积分基础上,引入了双区间值函数的Mcshane积分.其次,将模糊值函数的Mcshane积分推广为双枝模糊值函数Mcshane积分,并研究了此积分的一些基本性质.最后,结合双区间值函数和双枝模糊值函数的Mcshane积分定义,讨论了双枝模糊值函数的Mcshane积分的单调收敛定理和控制收敛定理.第二部分：利用无穷区间上传统的δ-精细分划定义,结合模糊值函数与其截函数之间的关系,引入了无穷区间上模糊值函数的Mcshane积分.此外,针对模糊值函数给出了等度模糊Mcshane积分定义,并给出了其模糊值函数可积的等价条件.最后,定义了强模糊Mcshane积分,并在此积分意义下获得了其模糊值函数可积的充分必要条件,从而完善并丰富了模糊积分理论.更多还原

【Abstract】 The paper mainly has two parts.The first part:at first, based on Mcshane integral of interval-valued func-tions, Mcshane integral of both-branch-interval-valued functions is introduced. Then Mcshane integral of fuzzy-valued functions is extended to both-branch-fuzzy-valued functions and some of its basic properties are studied. At last, com-bining the definitions of both-branch-interval-valued functions and both-branch-fuzzy-valued functions, monotone convergence theorem and dominated conver-gence theorem for Mcshane integral of both-branch-fuzzy-valued functions are discussed.The second part:using the definition of traditional fine division on infinite interval and combining the relationship between fuzzy-valued functions on in-finite interval and its cut functions, Mcshane integral of fuzzy-valued functions on infinite interval is introduced. Furthermore, aiming at fuzzy-valued functions, the definition of equivalent measure fuzzy Mcshane integral and a condition of equivalence of its integrability are given. Last but not least, strong fuzzy Mcshane integral is defined and in the sense of this integral a necessary and sufficient condi-tion for its fuzzy valued function to be integrable is obtained. Thereby the theory of fuzzy integral is improved and enriched.更多还原