数值函数

The definition of the absolute value for a fuzzy number is obtained.Furthermore,a lot ofproblems,such as absolute integrability,bounded variation and absolute continuity,arepresented and discussed.The representation theorem of the absolute values of fuzzy num-bers is established.It plays an important role in discussing the problems conceming theabsolute value.The relation between the absolute integrability and integrabili-ty is discussed,and the following result is obtained:aintegrable fuzzy-number-valued function is absolutely integrable iff it is integrable.The relation between theabsolute integrability and the absolute continuity of the primitive for fuzzy-number-valuedfunctions is dealt with.It is also pointed out that a fuzzy number valued function is ab-solutelyintegrable if and only if its integral primitive is fuzzy absolutely continuous.

提出了模糊数绝对值的概念并讨论了与绝对值相关的一系列问题，如绝对可积性、有界变差性、绝对连续性等，给出了模糊数绝对值的定义以及表示定理，该表示定理在涉及绝对值问题的讨论中起非常重要的作用；讨论了绝对可积与可积之间的关系，得到了结论：可积的模糊数值函数绝对可积的充要条件是该模糊数值函数可积；给出了模糊数值函数绝对可积与其积分原函数绝对连续性之间的关系，指出模糊数值函数绝对可积的充要条件是其原函数模糊绝对连续。

In addition, the properties and the characteristic theorems of this kind of integral are discussed by means of studying abstract functions in Banach space.

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。

In Chapter 2, one kind of rational cubic spline interpolation with linear denominator has been proposed, whose derivatives are replaced with accurate derivative values, difference quotient and arithmetic average difference quotientrespectively.

第二章给出了一类分母为线性的有理三次插值函数，当其导数值分别取为导数的精确值，一阶差商，以及算术均差商时，便得到三种插值格式，分别为给定导数值的有理三次插值函数，基于函数值的有理三次插值函数，以及基于算数均差商的有理三次插值函数。

Using the equivalent condition under which the limit of a sequence of fuzzy numbers exists in the sense of level convergence, we analyze the structure of the level continuous fuzzy number valued function. On the basis of it, we prove the level continuous fuzzy number valued function on a closed interval exists supremum and infimum and give the precise representation.

利用模糊数序列水平收敛意义下极限存在的充要条件，在分析了水平连续函数结构特点的基础上，证明了闭区间上水平连续的模糊数值函数存在上、下确界，并给出了上、下确界的具体表达式。

And we also study the absolute integrability and continuity of fuzzy-number-valued functions in the plane under consideration of different derivate bases.

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。

Using the concept of locally mean inte-grability which we give,we investigate the differentiability of the integral primitives.

对于模糊数值函数的导数问题进行了较为深入的探讨，尤其是积分原函数的可导性问题。

And using the embedding theorem, we get the characterizations ofmeasurability, differentiability and integrability of fuzzy n - cell number valued mappings.

并利用此嵌入定理给出了模糊n-方体数值函数的可测性，可导性和可积性的刻划。

-integrals of vector valued functions on infinite interval

无穷区间上n维模糊数值函数的积分：背景，定义及刻划

Since access to numerical function values is not presumed.

另一个直接搜索法特征的推论是它排除了逼近f的正常方法，不需要使用数值函数的值。

Based on this and the relations between integral and integral, integral and Riemann integral are established.

在此基础上讨论了非紧模糊数值函数的积分与积分之间的关系，以及积分与Riemann积分的关系。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。