点态化的模糊幂群

文献[1]提出了点态化Fuzzy集的概念,本文利用文献[1]中定义的Fuzzy点来研究Fuzzy幂群的性质和结构.得到了一些有关Fuzzy幂群的新结果.     

点态化Fuzzy幂群的转移定理

从F uz zy点的角度来研究F uz zy幂群,建立F uz zy幂群的转移定理,然后通过转移定理将分明幂群的许多概念和结论直接转到F uz zy幂群,揭示了F uz zy幂群与分明幂群的关系。     

Fuzzy幂群

文［１］讨论了代数结构的提升问题，提出了幂群的概念。模糊数学的发展要求各种数学结构不但要由论域向其幂集上提升，而且还要求向模糊幂集上提升，在更广泛的意义下讨论其结构问题，本文首先提出Ｆｕｚｚｙ幂群的概念，讨论了Ｆｕｚｚｙ幂群的结构及其同态问题。     

幂群的结构及其相互关系

§1 预备知识为了使本文自成一体,先介绍一些必备的定义和定理。定义1.1 设G是一个群,在(G)\{}中引入代数运算:A·B={a·b|a∈A,b∈B}。如果一个非空集族((G)\{(}对上运算作成群,我们称为G上幂群,其单位元用E来表示。定义1.2 设为幂群,若e∈E,其中e为G中单位元,则称为G的正则幂群。定理1.1 如果为G上的一个幂群,用|A|表示A的元素个数,则     

幂群所诱导的L－Fuzzy幂群

本文在幂群［１］的基础上，提出了幂群所诱导的Ｌ－Ｆｕｚｚｙ幂群、Ｌ－Ｆｕｚｚｙ幂群的λ－截、次幂群等—系列概念，并给出了幂群与其诱导的Ｌ－Ｆｕｚｚｙ幂群、λ截集群间的次同态、同态等关系。     

幂群所诱导的L—Fuzzy幂群

本文在幂群［１］的基础上，提出了幂群所诱导的Ｌ－Ｆｕｚｚｙ幂群、Ｌ－Ｆｕｚｚｙ幂群的λ－截、次幂群等一系列概念，并给出了幂群与其诱导的Ｌ－Ｆｕｚｚｙ幂群、λ截集群间的次同态、同态等关系。     

广义幂群及其构造

引入了广义核和广义幂群的概念，刻画了广义幂群的结构，并给出了广义幂群的构造定理。     

Fuzzy幂群的基数定理

文（１）提出了幂群的概念，给出了幂群中各元素是等势的基数定理，文（２）提出了Ｆｕｚｚｙ幂群的概念，但没研究其中各元素的基数问题，本文深入研究这一问题，得到了由Ｄ．Ｄｕｂｏｉｓ等在文（３）中提出的和由李洪兴等在文（４）中提出的两种Ｆｕｚｚｙ集基数形式下的Ｆｕｚｚｙ幂群的基数定理，并给出了Ｆｕｚｚｙ幂群中与基数有关的若干结果。     

F幂群的性质与结构

文[1]首次提出了F幂群的概念，并讨论了F幂群的基本结构及同态问题。本文进一步系统地讨论了F幂群的性质与结构。     

幂群的结构与分类

完整地研究了各种幂群的结构，对幂群进行了分类，并构造了各类的子群列和正规子群列。     

模糊商群的推广

引入关于一个子群的正规模糊子集概念，研究正规模糊子集的一些性质，并在此基础上将模糊商群做了自然推广，最后建立群同态下正规模糊子集的对应定理。     

基于模糊二元运算的直觉模糊群

为了使直觉模糊群也具有经典的结构,首先给出经典集合G的一种直觉模糊二元运算,利用这种直觉模糊二元运算定义了直觉模糊群,讨论这种直觉模糊群的一些性质,并给出直觉模糊群的两种等价定义。由于直觉模糊群具有和群一样经典的结构,因此,使直觉模糊代数的深入研究有了充分的理论基础。     

群中模糊同余关系下的模糊粗糙群

在模糊同余关系下，首次提出了群中模糊同余关系下的模糊粗糙集和模糊粗糙群的概念，并讨论了它的一系列的性质，得到了一些有意义的结果。     

Fuzzy preference orderings in group decision making

In this paper, some use of fuzzy preference orderings in group decision making is discussed. First, fuzzy preference orderings are defined as fuzzy binary relations satisfying reciprocity and max-min transitivity. Then, particularly in the case where individual preferences are represented by utility functions (utility values), group fuzzy preference orderings of which fuzziness is caused by differences or diversity of individual opinions are defined. Those orderings might be useful for proceeding the group decision making process smoothly, in the same manner as the extended contributive rule method.     

模糊粗糙群

研究模糊群的粗糙近似。借助模糊正规子群生成群上模糊近似空间,在模糊粗糙集模型的框架中对相关的模糊粗糙近似算子进行讨论。得到了模糊粗糙近似算子的基本性质,并研究了模糊粗糙近似算子与群中乘法运算的相容性。     

模糊自动机的强连通性及群自动机

为了更好地研究模糊自动机的结构和性质,采用代数的方法,在传统的模糊有限状态自动机的基础上,通过定义状态集合为代数群的自动机,讨论了这一类自动机的连通性和正则性,这丰富了模糊自动机理论．     

On regularity of block triangular fuzzy matrices

Necessary and sufficient conditions are given for the regularity of block triangular fuzzy matrices. This leads to characterization of idempotency of a class of triangular Toeplitz matrices. As an application, the existence of group inverse of a block triangular fuzzy matrix is discussed. Equivalent conditions for a regular block triangular fuzzy matrix to be expressed as a sum of regular block fuzzy matrices is derived. Further, fuzzy relational equations consistency is studied.     

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。     

Interval-valued intuitionistic fuzzy combined weighted averaging operator for group decision making

Determining the attribute weights, in the multiple attribute group decision-making analysis with interval-valued intuitionistic fuzzy information, plays a crucial role because of its direct effect on the optimal alternative. In this paper, we develop a new attribute weight based on the support and entropy measure of attribute values. Then, the interval-valued intuitionistic fuzzy combined weighted averaging (IVIFCWA) operator is proposed and its some primary properties are discussed. The IVIFCWA operator’s attribute values take the form of interval-valued intuitionistic fuzzy numbers and the principal component of the interval-valued intuitionistic fuzzy number is fully taken into account. Finally, a numerical example concerning the investment strategy is given to illustrate the validity and applicability of the proposed method.     

A study of normal fuzzy subgroups and characteristic fuzzy subgroups of a fuzzy group

In this paper, we investigate the properties of normal fuzzy subgroups of a fuzzy group. We also introduce the notion of a characteristic fuzzy subgroup of a fuzzy group, of which we provide level subset and strong level subset characterizations. Then we prove that a characteristic fuzzy subgroup of a fuzzy group is a normal fuzzy subgroup. Besides we prove that the commutator subgroup generated by the commutator of two normal fuzzy subgroups of a fuzzy group is contained in their intersection. Finally, we construct many new lattices and sublattices of fuzzy subgroups and normal fuzzy subgroups of a given fuzzy group. We also construct lattices of characteristic fuzzy subgroups possessing sup-property.