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On the whole, we do as follows: Firstly, we list some conceptions and lemmas for later use. Secondly, we inducted the absolute value norm in the two-dimensional vector interspace, and also proved the two-dimensional vector interspace is a Banach Interspace. Thirdly, we define two-dimensional vector-valued functions on a interval by the definition of -fine partitions in part 1. Then, some sufficient and necessary conditions of integrabel are given, and discuss the property of the integral on two-dimensional vector-valued functions.

主要包括以下内容：在第一部分，我们介绍了本文所用到的几个基本概念和引理；第二部分，我们在二维向量空间中引入了绝对值范数，并且证明了二维向量空间是一个Banach空间；在第三部分中，通过第一部分关于-精细分划的定义，我们给出了在某区间上二维向量值函数积分的定义以及可积的充分必要条件，并讨论了二维向量值函数积分的一些性质。

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。

Now that the L-valued fuzzy state automata has such powerful computation capacity, it is necessary to traverse the algebraic properties such as transformation semigroups,products and covering relations in L-valued fuzzy automata in order to show the close correspondence between the algebraic properties and the latticeordered monoid.

既然格值自动机具有如此强大的计算能力，有必要对其从代数角度出发较详细地，较深入地研究此类自动机的变换半群，乘积和覆盖关系，揭示此类自动机的代数性质和格半群间的紧密联系。

The algorithm used to implement fast Fourier transform of real-valued with complex-valued Fourier algorithm and the algorithm used to compensate the decaying direct current with arbitrary decay time parameter are deduced in detail.

对其中的一种用复序列DFT算法分析实数序列的算法和一种用来对具有任意衰减时间参数的衰减直流分量进行补偿的算法进行了详细推导。

We utilize the interval-valued intuitionistic fuzzy weighted arithmetic averaging operator to aggregate the interval-valued intuitionistic fuzzy information corresponding to each alternative, and then rank the alternatives and select the most desirable one according to the score function and accuracy function.

然后对权重信息未知的区间直觉模糊数的多属性决策方法进行了研究，给出了一个基于最大偏差的目标规划模型，从而获得相应的属性权重，基于IIWAA算子对区间直觉模糊数信息进行集结，进而根据得分函数和精确函数对方案进行排序。

Analysis is conducted on model checking for three valued logic formulae of modal transition system using existing model checking techniques. We reduce the three valued logic model checking problem for modal transition system to the two valued model checking problem under Kripke structure. This reduction is linear in the number of states, size of transition relations, and number of atomic propositional formulae in the new formed model compared with those in the original model. It does not increase the comple...

分析了现有的模型检验技术应用于模态转移系统的三值逻辑公式的模型检验中存在的问题·提出了把模态转移系统转换成Kripke结构的算法以及三值逻辑公式转换成2个二值逻辑的算法，经过转换后可用现有的模型检验技术进行模型检验·用该算法转换后，状态数、转移数和原子命题数目与原模型呈线性关系，没有增加模型检验的复杂度

In three-valued neural networks model, the energy function of two-valued neural networks model can not be applied, so the energy function need to be find for the three -valued neural networks model, and here two kind model algorithms are compared in this paper.

在三值神经网络模型中，二值模型的能量函数不能适用于三值模型，因此需要求解三值模型的能量函数，在此本文对三值神经网络测试生成算法与二值神经网络测试生成算法进行比较。

In this paper,some equivalence properties of one-valued selection under the set-valued mapping is introduced and give a sufficient and necessary condition of set-valued mapping being a metric projection.

介绍了集值映射的单值选择的几个等价性质，并给出了集值映射成为度量投影的一个充要条件。结果将度量投影情形推广到了集值度量投影情形

As a special case, we studied the resolution-like procedures of lattice-valued Horn-clause with truth-value in lattice implication algebra, and discussed the lattice-valued Prolog language based on that kind of lattice-valued Horn-clause.

作为特殊情形，特别研究了基于格蕴涵代数的格值Horn子句的类归结方法，并对建立其上的格值Prolog语言作了一定的探讨。

Furthermore we introduce the concepts of coverings and lattice-valued homomorphisms,we prove that the L-valued fuzzy transformation semigroups in which the multiplication is fuzzy transformation semigroup inducible is equivelent to usual faithful transformation semigroups in the sence of lattice-valued strong homomorphism.

若格半群中的乘法是格值变换半群可诱导的，在格值强同态下证明了格值可诱导变换半群和一般有效变换半群是等价的。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。