1、

Based on the atoms and congruence relations of approximation algebra, it is proved that rough set algebra becomes pseudo-complemented MS algebra if proper complement operators are selected.

借助近似代数上的原子及同余关系,证明了在适当选取余运算之后,粗集代数就构成伪补MS代数。

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2、

different classes of rough fuzzy set algebra are obtained from different types of binary crisp relations. in the axiomatic approach, one defines a pair of dual rough fuzzy approximation operators and states that axioms must be satisfied by the operators.

在公理化方法中,用公理形式定义了粗糙模糊近似算子,各种类型的粗糙模糊集代数可以被各种不同的公理集所刻画。

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3、

Crawley-Boevey introduced the conception of exceptional sequence to the representation theory of path algebra. He has shown that the braid group acts transitively on the set of complete exceptional sequence.

Crawley-Boevey将例外序列的概念引入路代数的表示理论中,并证明了辫子群对路代数的模范畴中的完备例外序列的作用是可迁的。

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4、

In FLn, the standard set of truth-values is the unit interval [ 0,1] and the truth functions of connective make it to be an algebra of truth degrees.

FLn的标准真值集为单位区间[0,1],并且联结词的真值函数使得[0,1]成为一个真值代数。

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5、

This paper studies and discusses the application of rough set theory on algebra system-group basically, intro-duces such concepts as rough subgroup and rough ideals, points out and gives proof of several related properties.

文章主要讨论粗糙集理论在代数系统&群上的应用,引入了粗糙子群与粗糙理想等概念,提出并证明了与此相关的性质。

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6、

The corresponding mathematic model involved a set of nonlinear equations is solved by the GAMS ( general algebra model system) software tool. This method could achieve minimal fresh water use and optimal network assignments simultaneously.

该超结构的数学模型为一组非线性方程,可以利用GAMS等数学软件进行求解,得到各个周期的最小新鲜水量和最优的用水网络结构。

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7、

a semilattice can be defined as a universal algebra, and it can also be defined as a partial ordered set.

一个半格可以定义为一个泛代数,也可以定义为一个偏序集。

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8、

in this paper, we proved that the definition of a semilattice as a universal algebra and the definition of a semilattice as a partial ordered set are equivalent.

本文中,我们证明了作为泛代数的半格的定义与作为偏序集的半格的定义是等价的。

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9、

The adjoint algebra of partial order set

关于偏序集的伴随代数

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10、

WIS Algebra and I Ideals Generated by a Set in WIS-Algebra

WIS代数及其由WIS代数中的子集生成的I理想

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12、

Based on the attributes' importance degree theory of rough set, a new weighted naive Bayes method is proposed. Methods for determining the weights of attributes in the algebra view, informational view and both of them are developed respectively.

基于Rough Set的属性重要性理论,提出了基于Rough Set的加权朴素贝叶斯分类方法,并分别从代数观、信息观及综合代数观和信息观的角度给出了属性权值的求解方法。

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13、

on the relationship among universal set, universal logic and universal algebra

论泛集合、泛逻辑和泛代数的关系

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14、

boolean algebra based on the two new operations in the rough set theory

粗糙集的两种新型算子及其Boolean代数性质

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15、

All the existing Methods : Utilize quaternion algebra to iteratively compute M-sets'boundaries.

用文中提出的体绘制算法绘制了三元数法和四元代数法所构造的三维M集.

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16、

Interpolation Set of Weak Function Algebra and Function Algebra

弱函数代数与函数代数的插补集

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17、

Finally, the 3-D M-sets generated by the ternary number and quaternion algebra are both rendered by our new algorithm.

用文中提出的体绘制算法绘制了三元数法和四元代数法所构造的三维M集。

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18、

Apply Lagrange equation of the first kind to the system, and get a set of the differential-algebraic equations ( DAEs) of its absolute coordinates.

对系统应用第一类拉格朗日方程,得到系统位形坐标的微分&代数方程组。

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19、

Firstly, the Ternary Logic Difference is introduced, then a complex model of arbitrary networks is set up on the basis of new ternary algebra, and finally, a new algorithm is presented, by which one can describe the transient process of a sequential circuit completely.

在新三值代数的基础上建立了任意网络的复数模型。最后,本文提出一个新算法,用此算法能完整地描述时序电路的过渡过程。

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