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Chapter 4 establishes the theory of convex fuzzy mappings: The concepts, such as Jensen's inequality, positively homogeneous, infimal convolution, right scalar multiplication and convex hull are introduced. The corresponding theorems are demonstrated by using the parametric representations of fuzzy numbers. In anti-fuzzy number space, the conjugate mapping of convex fuzzy mapping is concerned, and convexities of conjugate set and conjugate mapping of convex fuzzy mapping are proved. The notions of subgradient, subdifferential, differential with respect to convex fuzzy mappings are investigated, which provides the basis of the theory of fuzzy extremum problems.

在第4章中，建立了有关凸模糊映射的理论：建立了关于凸模糊映射的Jensen不等式、模糊正齐次映射、凸模糊映射的下卷积、右数乘和凸包等概念，利用模糊数的参数化表示，给出了相应的定理；在反模糊数空间，对凸模糊映射的共轭也作了探讨，证明了凸模糊映射的共轭集合和共轭映射都是凸的；最后对凸模糊映射的次梯度、次微分和微分等概念进行了研究，为模糊极值理论打下了基础。

Laws must be sufficient to determine the will as will, even before I ask whether I have power sufficient for a desired effect, or the means necessary to produce it; hence they are categorical: otherwise they are not laws at all, because the necessity is wanting, which, if it is to be practical, must be independent of conditions which are pathological and are therefore only contingently connected with the will.

简译：laws必须足以把意志作为意志来规定，即使并没有进行这个（即'我问我自己是否拥有足以实现所欲求的后果的能力或产生该后果所必须的工具'）；因此它们是范畴性的categorical定言的，否则它们就不是laws，因为它缺乏必然性，而如果这个原理要被实践的话，这必然性是和'诸如习惯喜好等（由此是偶然关联于意志的）条件'无关的/相独立的。

In this dissertation,Von Numann and Morgenstern Axioms are analyzedagain at first.It is pointed out not only that preference relations are often latticeordered,but also that the transitivity axiom,along with the independence axiomand the continuity axiom is still rational to a high degree,then a new set ofaxioms for lattice-order decision-making behavior is established.At last,relatedsubjects based on lattice in preference theory,utility theory,decision-makingmethods,multiattribute decision-making,and group decision-making are studied.In this way,the lattice-order decision-making theory is framed.Main creativeresults are obtained as follows

本论文重新审视了Von Neumann-Morgenstern理性行为公理体系，对以前学者较少涉及到的连通性公理提出了质疑，指出偏好关系具有格特征，而传递性公理、独立性公理以及连续性公理在很大程度上仍具有合理性，进而创建了格序决策行为公理体系，研究了基于格的偏好理论、效用理论、决策方法、多目标决策以及群决策中的相关问题，初步构建了格序决策理论框架，主要研究成果如下

The properties of the new method are that (1) the equations that the quartic Bézier curve has to satisfy for being C 2 continuous are strictly row diagonally dominant;(2) the discontinuous points of the curve are at the given data points;(3) the curve is locally adjustable;(4) if the given data points are convex, the constructed quartic Bézier curve is convex.

用样条函数方法构造插值样条曲线曲面，曲线曲面的精度和形状是由给定的数据点和端点条件唯一确定的。在有些情况下，例如，对文献 [7～ 9]中的数据点集，由样条函数方法构造的C2 插值曲线是不可接受的，但由于没有额外自由度，无法调整曲线的形状。

S, I just work into the city, the unit assigned to me in a hostel in Xitang river, though small, but I open the east window, is facing Xitang River, the river at that time Xitang River, there is south to north to the business of the vessel, there are regularly-scheduled passenger ships, there are stow net income of small fishing cards, there are doing small business of the coppersmith vessels, but also to the boat for home, household vessels, the river there are raft, rafts, day boats coming and going, noisy noisy.

70年代，我刚进城工作，单位分配给我的宿舍就在西塘河边，尽管很小，可我推开东窗，面临的就是西塘河，那时的西塘河河面上，有南来北往经商的货船，有定时定班的客船，有张网收卡的小渔船，有做着小本生意的铜匠船，也有以船为家的住户船，河里有木排、竹排，白天船只来往穿梭，喧闹吵杂。

Firstly, the self-owned business hall, one to one marketing channel and 1860 hotline are core. Secondly, franchising store, bank cooperation and post cooperation are main body. Thirdly, specified distribution store and its subsidiaries are main selling power. Fourthly, network business hall, self-help service system and phone-bundled distribution are new type service channels. Lastly, establish the multi-channels that the above-mentioned models exist together.Constructing the informative service marketing channels, utilizing the promoting and controlling methods, improving the efficiency of managing service marketing channels and the loyalty degree of social marketing channels, in a result, form the core competitiveness of Hunan Mobile Communication Company.

针对各种模式所服务的用户群体和服务手段，提出了以自办营业厅、一对一直接渠道和1860客户服务热线为核心，特许经营店和银行邮政合作为服务主体，指定专营店及其下辖的普通代理店等为主要销售力量，网上营业厅、自助服务系统和手机捆绑销售等为新型营销服务形式的多种形式并存的混合型服务营销渠道模式，以服务营销渠道信息化为手段，采取相应的激励和控制方法，提高服务营销渠道的管理效率和社会营销渠道的忠诚度，营造湖南移动通信公司的核心竞争优势。

The machine for oriental Sixiang corporeity diagnosis are widely used in the hospitals of oriental medicine in Korea.These machines are not perfect,but they are accepted by patients and doctors,which are constantly improved.

韩医为四象体质诊断所研发的仪器在韩国医院被广泛应用，这些仪器虽不是很完善，但在医疗实践中被病人所接受，被医生认可，并不断被改进。

Firstly, Some of the basic concepts of chaotic vibration are introduced, the qualitative and quantitative methods of chaotic vibration identification are detailed, the selection of associated parameters is studied, the algorithms for calculating the maximum Lyapunov exponent, correlation dimension and periodicity ratio are provided. On the basis of analysis and comparison of different methods, the methods used in the paper are selected.

本文首先介绍了混沌振动的基本概念；评述了混沌振动识别的定性和定量方法；对有关参数的选择进行了研究；给出了计算最大Lyapunov指数、相关维数和周期比的算法；在对不同方法对比分析的基础上，选出了本文拟采用的识别方法。

In a method for retrieving sequences having a minimum PAPR in an OFDM (orthogonal frequency division multiplexing) system, by using characteristics in which all sequences of the OFDM system are classified into cosets having the same PAPR, PAPRs of sequences in which early two elements are fixed as '0' are calculated. A sequence having a minimum PAPR is selected from among the calculated PAPRs, and sequences allocated to the coset in which the selected sequence is included are retrieved as sequences having the minimum PAPR.

在一种用于在OFDM通信系统中恢复具有最低PAPR的序列的方法中，通过利用在其中将OFDM系统的所有序列分成具有相同PAPR的同余类序列的特性，计算两个开始项被固定为"0"的序列的PAPR，在所计算的PAPR中选择具有最小PAPR的序列，并且恢复分配至在其中包含所选同余类序列的序列作为具有最小PAPR的序列。

This approach not only inherits the advantages of absolute density based algorithms which can discover arbitrary shape clusters and are insensitive to noises , but also efficiently solves the following common problems: clustering results are very sensitive to the user-deflned parameters, reasonable parameters are hard to be determined, and high density clusters are contained fully in coterminous low density clusters. With this approach, incremental clustering can also be supported effectively by defining the affected sets and seed sets of the updating objects in this approach.

聚类算法的有效性问题主要表现在三个方面：其一，聚类算法大多要求用户输入一定的参数，例如希望产生的簇的数目，而这些参数通常难以确定，特别是针对高维空间中稀疏分布的实际应用数据集，用户几乎无法给出合适的算法参数，因此非专业用户需要与数据分析专家密切配合才能保证获得理想的聚类结果，导致算法的使用极为不便；其二，聚类结果对于输入的参数值过于敏感J，往往参数值的一些轻微变化却产生聚类结果的很大差异；其三，对于高维的实际应用数据集，其数据分布往往是稀疏的、杂乱的，很难为算法选择全局的参数进行准确的聚类分析，使得聚类的质量难以保证。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。