基于相对熵的不完全信息群体专家权重的集结

针对属性权重信息和属性效用信息都不完全的群体多属性决策问题,运用相对熵理论提出了一种专家权重的确定方法．该方法通过集结各方案的综合评价值向量,客观地得到专家的权重,避免系统聚类方法中由给定相似度水平归类而产生的主观性问题．应用实例表明了方法的有效性和实用性．     

基于TOPSIS的区间三角模糊集群决策方法

在多属性决策方法中,因为每个专家都有他自己的知识和专长,因此对于不同的属性不同的专家就会有不同的权重.在区间三角模糊集上提出了一种基于TOPSIS的确定专家权重的新方法.该方法在评价值接近正理想点并且同时远离负理想点时会被赋予一个较高的专家权重;反之,评价值就会被赋予一个小的专家权重;经验证,通过该方法确定的专家权重对于解决实际的决策问题效果显著.进而提出了一种属性权重信息在不同情形下的区间三角模糊集多属性群决策方法:包括属性权重完全已知,部分已知和完全未知,并且通过实例验证了该方法的可行性和有效性.     

基于直觉模糊软信息的多属性群决策方法

针对属性权重和专家权重信息都完全未知的多属性群决策问题,提出了一类以直觉模糊软集为数据环境的群决策方法。通过提取理想点结合距离测度构建非线性规划模型来求解属性权重。利用得分函数进行矩阵变换,基于各对象的综合正、负理想值构造满意度,并根据总体满意度最大化原则构建规划模型确定专家权重。最后利用属性权重和专家权重对得分矩阵进行加权平均,计算各对象的综合得分,进而给出具体的多属性群决策过程,并实例验证了决策方法的可行性和合理性。     

一种基于Shapley值的Pythagorean模糊多属性群决策方法及其应用

针对模糊决策信息环境下的专家权重确定问题提出一种基于Shapley值的Pythagorean模糊多属性群决策方法。本文引入Shapley值和特征函数的定义,提出Pythagorean模糊距离测度和Pythagorean模糊决策误差信息矩阵等概念,并研究它们的性质。进一步,构建基于Shapley值的Pythagorean模糊专家权重确定模型和属性权重确定模型。针对决策信息是以Pythagorean模糊数形式给出的决策问题,提出一种基于Shapley值的Pythagorean模糊多属性群决策方法,并应用到应急救援中,验证了该方法的有效性。     

一种区间Pythagorean模糊VIKOR多属性群决策方法

针对属性信息为区间Pythagorean模糊集且属性权重和专家权重均未知的一类群决策问题, 结合信息熵理论, 提出了一种区间Pythagorean模糊VIKOR多属性群决策方法。首先定义一种新的区间Pythagorean模糊距离测度, 并讨论其性质。其次基于该距离测度定义了区间Pythagorean模糊相对距离指数, 并基于相对距离指数构建了一种熵权模型确定专家权重和属性权重。然后提出一种区间Pythagorean模糊VIKOR多属性群决策方法。最后通过企业生产方案选择案例说明了提出新方法的可行性与有效性。     

属性和专家客观权重未知的多值中智数群决策方法

针对评价信息为多值中智数的多属性决策问题,提出基于最小最大相似度求解属性权重与标准区间求解专家权重的方法.该方法首先根据最小最大模型求解属性权重,将初始评价矩阵集结为综合决策矩阵,其次利用数字分析法求得标准区间,根据各专家与标准区间的相似度确定专家权重,再对综合评价矩阵集结得各方案的综合评价值,对综合评价值排序得最优方案,最后用实例说明了方法的有效性和适用性.     

基于先验信息和一维数据聚类的专家赋权方法

多属性群体评价方法研究中,对专家赋权是一项重要的研究内容。本文结合专家的先验信息和后验信息,提出了一种确定专家权重的方法。首先,利用专家历史评价活动中的序值相关系数,做出本次评价活动的预测值,进而确定专家先验权重;其次,基于群体共识视角,对各专家所给出的指标信息进行一维数据聚类,结合不同分组情况下出现的概率,计算出专家后验权重;最后,将两类权重进行组合确定最终权重,并用一个算例验证了该方法的有效性以及合理性。     

模糊环境下部分权重信息的多属性群决策方法

针对决策过程中信息是模糊不确定的,属性的权重信息是部分可知的,我们给出了一个新的确定不同专家给出的属性值的权重的方法.该方法能将靠近中心值的属性值分配较大的权重,而给远离中心值的属性值分配较小的权重,从而得到更加合理的综合属性值.为了确定属性的权重信息,我们建立了一个线性规划模型.利用所给的新方法,我们给出了一个新的模糊多属性群决策方法.最后的实例说明方法的有效性和合理性.     

毕达哥拉斯群决策方法及其在绿色供应商选取中的应用

针对专家权重未知且属性值为毕达哥拉斯模糊数的多属性群决策问题,基于证据理论和混合加权毕达哥拉斯MSM算子,提出了一种群决策方法。 首先,由决策信息矩阵获取专家的模糊测度,并赋予其相应的权重;其次,基于新构造的混合加权毕达哥拉斯MSM算子对专家所提供的属性信息分别进行集结,得到各个专家的综合评价信息;再次,利用证据合成方法,对专家综合评价信息进行融合,获得候选方案的综合证据信息,进而可知备选方案的信任区间,并据此对候选方案进行优选决策;最后,绿色供应商选取案例的分析与对比验证了方法的可行性与合理性。     

基于TOPSIS的三角模糊集群决策方法

在多属性群决策方法中,决策者的权重对排序结果是非常重要的,并且已经得到了人们越来越多的重视。在三角模糊集的基础上提出了一种基于TOPSIS的确定专家权重的新方法。进一步定义了三角模糊数的一些基本概念,提出了一种属性权重信息在不同情形下的三角模糊数多属性群决策方法,包括属性权重完全已知、部分已知和完全未知。最后用实例证明了该方法的可行性和有效性。     

Equality of orthogonal transvection group and elementary orthogonal transvection group

H. Bass defined orthogonal transvection group of an orthogonal module and elementary orthogonal transvection group of an orthogonal module with a hyperbolic direct summand. We also have the notion of relative orthogonal transvection group and relative elementary orthogonal transvection group with respect to an ideal of the ring. According to the definition of Bass relative elementary orthogonal transvection group is a subgroup of the relative orthogonal transvection group of an orthogonal module with hyperbolic direct summand. Here we show that these two groups are the same in the case when the orthogonal module splits locally.     

Twisted second homology groups of the automorphism group of a free group

In this paper, we compute the second homology groups of the automorphism group of a free group with coefficients in the abelianization of the free group and its dual group except for the 2-torsion part, using combinatorial group theory.     

Zero entropy subgroups of mapping class groups

Given a group action on a surface with a finite invariant set we investigate how the algebraic properties of the induced group of permutations of that set affects the dynamical properties of the group. Our main result shows that in many circumstances if the induced permutation group is not solvable then among the homeomorphisms in the group there must be one with a pseudo-Anosov component. We formulate this in terms of the mapping class group relative to the finite set and show the stronger result that in many circumstances (e.g. if the surface has boundary) if this mapping class group has no elements with pseudo-Anosov components then it is itself solvable.     

Graded group schemes and graded group varieties

We define graded group schemes and graded group varieties and develop their theory. Graded group schemes are the graded analogue of a?ne group schemes and are in correspondence with graded Hopf algebras. Graded group varieties take the place of infinitesimal group schemes. We generalize the result that connected graded bialgebras are graded Hopf algebra to our setting and we describe the algebra structure of graded group varieties. We relate these new objects to the classical ones providing a new and broader framework for the study of graded Hopf algebras and a?ne group schemes.     

The permutation class group of a finite group

Analogously to the projective class group, the permutation class group of a finite group π can be defined as the group of equivalence classes of direct summands of integral permutation modules modulo permutation modules. It is shown that this group behaves nicely with respect to localization and completion, which then is used to prove that contrary to the projective class group - it is not always a torsion group. More precisely, the rank of the permutation class of group is computed.     

Coorbits of Quantum Homogeneous Spaces

The notion of coorbits for spaces with quantum group actions is introduced. A space with a quantum group action is given by a pair of algebras: an associative algebra which is the analog of a classical topological space, and a Hopf algebra which is the analog of a classical topological group. The Hopf algebra acts on the associative algebra via a comodule structure mapping which is also an algebra homomorphism. For a space with a quantum group action, a coorbit is a pair of spaces given by the image and the kernel of an algebra homomorphism from the associative algebra to the Hopf algebra. The coorbits of several types of quantum homogeneous spaces are discussed. In the case when the associative algebra is the group algebra of a group and the Hopf algebra is a quotient of the group algebra, the connection between the set of coorbits and the character group is established.     

The Lie Group Structure of the Butcher Group

The Butcher group is a powerful tool to analyse integration methods for ordinary differential equations, in particular Runge–Kutta methods. In the present paper, we complement the algebraic treatment of the Butcher group with a natural infinite-dimensional Lie group structure. This structure turns the Butcher group into a real analytic Baker–Campbell–Hausdorff Lie group modelled on a Fréchet space. In addition, the Butcher group is a regular Lie group in the sense of Milnor and contains the subgroup of symplectic tree maps as a closed Lie subgroup. Finally, we also compute the Lie algebra of the Butcher group and discuss its relation to the Lie algebra associated with the Butcher group by Connes and Kreimer.     

两类Cayley的向图的同构问题

证明了对m=1,2,3,有限广义双循环群B(Q8)是m-DCI群当且仅当它的极大交换子群L是m-DCI群且4|-1mm|L|;有限广义二面体群D是m-DCI群当且仅当它的极大交换子群K是m-DCI群且2|-1mm|K|.     

Relative hyperbolicity and similar properties of one-generator one-relator relative presentations with powered unimodular relator

A group obtained from a nontrivial group by adding one generator and one relator which is a proper power of a word in which the exponent sum of the additional generator is one contains the free square of the initial group and almost always (with one obvious exception) contains a non-abelian free subgroup. If the initial group is involution-free or the relator is at least third power, then the obtained group is SQ-universal and relatively hyperbolic with respect to the initial group.     

Cluster automorphism groups of cluster algebras with coefficients

We study the cluster automorphism group of a skew-symmetric cluster algebra with geometric coefficients. We introduce the notion of gluing free cluster algebra, and show that under a weak condition the cluster automorphism group of a gluing free cluster algebra is a subgroup of the cluster automorphism group of its principal part cluster algebra (i.e., the corresponding cluster algebra without coefficients). We show that several classes of cluster algebras with coefficients are gluing free, for example, cluster algebras with principal coefficients, cluster algebras with universal geometric coefficients, and cluster algebras from surfaces (except a 4-gon) with coefficients from boundaries. Moreover, except four kinds of surfaces, the cluster automorphism group of a cluster algebra from a surface with coefficients from boundaries is isomorphic to the cluster automorphism group of its principal part cluster algebra; for a cluster algebra with principal coefficients, its cluster automorphism group is isomorphic to the automorphism group of its initial quiver.