等价关系

An independent axiomatic system that describes the upper approximation of Pawlak rough sets is formulated by three simple formulas.

获得的结果深刻地揭示了经典等价关系与模糊等价关系的本质区别，进一步深化了Pawlak粗集理论。

With regard to the section of coset in algebraic structure, a series of well-mastered concepts including equivalent relationship and division are applied, and typical examples are cited to introduce the conception of equivalent relationship-coset relationship defined through subgroup.

对于其中代数结构部分的陪集一节，应用已经熟知的等价关系和划分的概念，通过引例导出由子群定义的等价关系―陪集关系，进而得到群的划分―陪集，再研究陪集的性质。

Basic concepts of Equivalence Relations, Dynamic equivalence problem, Basic operations of equivalence class, smart algorithm.

等价关系的基本概念，动态等价问题，等价关系基本操作的实现，提高效率的方法。

Classic rough set theory based on equivalence relation takes complete system as object of study , and divides the region into some non-intersect equivalence class; But, in the real life, because of the errors in data measuring, understanding of data, or the restriction in data collection , it can make the decision-making system incomplete, that is, value of attribution of some objects is unknown, which restrains development of the theory to practical direction.

经典粗糙集理论以完备系统为研究对象，以等价关系为基础，通过等价关系将论域划分为互不相交的等价类；然而，在现实生活中，由于数据测量的误差，对数据理解或获取的限制等原因，使得在知识获取时往往面临的是不完备系统，即可能存在部分对象的一些属性值未知的情况，这就极大地限制了粗糙集理论向实用化方向发展。

The method evaluates relative similarity relation to each object to form initial equivalence relation,and the equivalence class is developed.

引入等价关系隶属度因子γ，用于度量等价关系间隶属关系，作为聚类过程一个有效参数，控制聚类的规模。

This equivalence relation, however, seems to be a very stringent condition that may limit the application domain of the rough set model.

此外，等价关系是经典粗糙集理论中最为关键和重要的概念，然而等价关系看起来是一个过强的条件，可能会限制了粗糙集模型的应用领域。

Rough set theory is developed based on the notion of equivalence relation,but the property of equivalence has limited its application fields,which may not provide a realistic description of real-world relationships between elements.

粗糙集理论是建立在等价关系的基础上发展起来的，但等价关系性质的应用领域是有限的，等价关系不能对现实世界中的元素关系给出客观的描述。

The defect of traditional classify approach is analyzed,the concept of fuzzy equivalent relations is given,the solution approach of fuzzy equivalent matrix is put forward,and the evaluation indexes system of emergency materials classification is built.On the basis of above discussing,the classify method of emergency materials based on fuzzy clustering analysis is developed.

分析了传统分类方法存在的问题，给出了模糊相似关系和模糊等价关系的概念和求模糊等价矩阵的方法，建立了应急物资分类指标体系，在此基础上提出了基于模糊聚类的应急物资分类方法。

Firstly, we focus on the influence of the inclusion of equivalent relation on the information entropy, which is explained through 8 propositions. Secondly, we also investigate the relation between the Shafer's evidence theory and equivalent relation.

又章主要从两方面进行论证：①等价关系的粗细对信息熵的影响，这点通过8个命题来说明；②等价关系与证据理论之间的联系。

Therefore, it's natural to estimate those values of operators such as 〓, log mf and so on in order to investigate the weighted inequalities for the minimal operator We discuss them under two conditions respectively: In one-weight case, we establish the relative weighted inequalities under the condition of A〓-weight and A〓-weight respectively, and the equivalent condition has been found between the strong -type weighted inequality and the property of W〓-weight; while in the case of two-weight condition, we characterize the equivalent relations between the weak type weighted inequality and the property of W〓-weight, the strong -type weighted inequality and the property of W〓-weight.

我们分两种情况分别加以讨论：单权情况下，我们分别刻画了A∞权和A〓权条件下关于〓，log mf等的强型加权不等式，并证明了关于鞅的极小算子的强型加权不等式与对应的W〓权性质之间的某些等价关系；在双权情况下，我们刻画了关于极小算子的弱型加权不等式与W〓权以及强型加权不等式与W〓权之间的等价关系。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。