论文标题:平面上模糊数值函数的Henstock积分
On Henstock Integral of Fuzzy-Number-Valued Function in the Plane
论文作者
论文导师 巩增泰,论文学位 硕士,论文专业 计算数学
论文单位 西北师范大学,点击次数 117,论文页数 57页File Size2180K
2007-05-01论文网 http://www.lw23.com/lunwen_99447772/
Derivate bases;; Fuzzy number;; Fuzzy-valued Function;; Integral;; Absolute integrability
基于模糊积分理论的研究和模糊微分方程求解的需要以及模糊随机变量期望的计算,本文研究了平面上模糊数值函数的积分。首先,作为δ-精细分法的推广,提出了平面上的精细分法,即定义了导数基并讨论了其性质。又在此导数基意义下定义了平面上模糊数值函数的Henstock积分,并利用Banach空间上的抽象函数对其进行了刻划。其次,定义了平面上的模糊Perron积分及模糊Denjoy积分,并利用这两种积分对平面上两种特殊形式的导数基意义下的模糊Henstock积分原函数进行了刻划。最后讨论了在不同导数基意义下的模糊数值函数的绝对可积性和连续性问题,完善了非绝对模糊积分理论。对于平面上模糊Henstock积分,利用近似求和、数学规划两种方法进行了计算和误差估计:提出了平面上模糊Henstock积分计算的矩形公式和Simpson公式等。
In this paper, the integral of fuzzy-number-valued functions in the plane is discussed. Firstly, as the generalization ofδ-fine partitions, the fine partition in the plane which is named derivate base is proposed, and the Hen-stock integral of fuzzy-number-valued functions in the plane is defined in the sense of the derivate base above. In addition, the properties and the characteristic theorems of this kind of integral are discussed by means of studying abstract functions in Banach space. Nextly, the definition of Perron integral and Denjoy integral for fuzzy-number-valued functions in the plane are given, and by using them, we discuss the characterization theorems of the primitive functions for fuzzy Henstock integral in the sense of the special derivate bases. And we also study the absolute integrability and continuity of fuzzy-number-valued functions in the plane under consideration of different derivate bases. Finally, for the fuzzy Henstock integral in plane, two calculating methods are proposed: one is to calculate directly by using the method of approximation including quadrature rules and the error estimates such as the rectangular rule and Simpson"s formular; another is to calculate by using the equivalent characteristic of fuzzy Henstock integrability, whose membership function could be obtained by solving nonlinear programming problem.
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