函数依赖集F有内部冲突的判定问题研究

在讨论数据库模式R(W，F)的无α环分解时，需要判定FD集F是否有内部冲突；在讨论无β，γ环的分解时也需要判定是否有内部冲突．为此，应当首先给出归并依赖集的二元组集合、闭包等概念；分别给出求解二元组集合及其闭包的多项式算法．在此基础上，讨论FD集F有内部冲突时的特征和相关条件，给出相应的有内部冲突的判定定理和算法，对算法进行了证明和分析．     

基于删除序偶的传递闭包求解算法

针对在已有传递闭包的基础上删除序偶后的传递闭包求解问题,提出一种基于传递闭包的传递闭包动态求解算法,给出了其形式化描述形式,并给出了算法的详细证明过程.该算法在已有的传递闭包基础上,通过把新删除序偶及该序偶的所有依赖间接指向序偶从已有传递闭包中删除实现求解过程,从而使算法的时间复杂度降低为O(n<'2>),并且不受稀疏矩阵或序偶链的链长等不确定因素影响,最后通过一个实例说明了该算法的执行过程.     

Petri网语言表达式及其求解算法

Petri网语言是描述网系统动作序列的集合.为了给出一个网系统语言的形式描述,基于Petri网的状态转换图,分析了Petri网的行为特征,定义了α闭包表达式和Petri网语言表达式,给出了求解Petri网语言表达式的算法,为Petri网语言的形式化描述和分析提供了一种新方法.     

基于逆向FD超图的属性闭包求解算法研究

本文对文⑴进行深入分析的基础上给出了正向ＦＤ超图、逆向ＦＤ超图，给出了正向、逆向超图的相互转换算法，并对属性闭包的求法进行了研究，给出了求解关系模式属性闭包的新算法。     

二元关系传递闭包的几种求取方法分析

本文给出了根据传递扩张原理、关系矩阵、关系复合运算、Warshall算法以及改进的Warshall算法等几种求解二元关系传递闭包方法,并分析了各自的特点,可帮助学生有效掌握求解二元关系传递闭包的运算。     

一种新的概念格并行构造算法

概念格作为形式概念分析理论中的核心数据结构,在数据挖掘和知识发现、人工智能、信息检索、粗糙集[1]等领域得到了广泛的应用。概念格的构造在其应用过程中是一个主要问题。提出了一种基于闭包系统划分的概念格并行构造算法——Para_Prun算法,它将概念集合看作初始闭包系统,引入了子闭包系统的有效性判断,迭代生成相互独立的多个子闭包系统,然后在每个子闭包系统中独立生成概念,有效地提高了概念的求解速度。最后用实验证明了算法的正确性和有效性。     

传递闭包求解的教学问题

根据离散数学课的难度，结合学生的接受能力。分别应用集合运算法、直观图示法、矩阵法等，由浅入深、从直观到抽象撂讨了传递闲包的求解，并讨论了Warshall算法的思想和在教学中运用，有利于改善传递闭包求解的教学效果。     

基于Prolog的二元关系闭包运算的研究与实现

在代数系统中,关系作为一种抽象工具,在计算机科学研究领域有着极其广泛的应用.文章在研究传统闭包求解方法的基础上,结合其思想给出了用人工智能语言Prolog实现传递闭包求解策略的思想与方法,并在实例中给予论证,此方法具有一定的典型研究意义及价值.     

基于矩阵的BCNF分解算法

本文以矩阵为工具,讨论了将矩阵运用到关系模式规范化过程中,用矩阵来表示函数依赖关系,利用矩阵求属性集合的闭包,给出了基于矩阵的BCNF分解算法。     

基于混合超图的最小覆盖,闭包求解算法研究

文中讨论了基于混合超图的有关冗余消除的部分定理，完善了这一理论。并给出了最小覆盖，闭包求解的新算法，进行了相关算法分析。     

区间直觉二元语言集成算子及其群决策方法

基于下标以零为中心对称的语言评估标度,将区间不确定二元语言集与区间直觉模糊集结合,提出区间直觉二元语言集及变量的概念;讨论区间直觉二元语言变量的运算及可能度;提出区间直觉二元语言加权算术平均算子、区间直觉二元语言有序加权平均算子,并在此基础上,通过可能度矩阵对区间直觉二元语言变量进行排序提出区间直觉二元语言混合加权平均算子;最后基于这些算子构建了一种新的直觉模糊多属性群决策方法,并将其运用于供应商选择过程中。     

2TLCGPOWA算子及其在多属性群决策中的应用

基于集对分析理论中二元联系数的不确定性,将联系变量引入到区间二元语义环境中,定义了二元语义联系变量,给出了二元语义联系变量的运算法则,并提出了几种新的算术集结算子。针对决策矩阵元素为区间二元语义变量和属性权重完全未知的不确定多属性群决策问题,提出了一种基于2TLCGPOWA算子的不确定多属性群决策方法。最后通过对某大学教师的任职和晋升考核来说明该方法的可行性和有效性。     

Some new Shapley 2-tuple linguistic Choquet aggregation operators and their applications to multiple attribute group decision making

In this paper, we investigate the multiple attribute group decision making (MAGDM) problems with 2-tuple linguistic information. Firstly, motivated by the ideas of Choquet integral and Shapley index, we propose three 2-tuple linguistic aggregation operators called Shapley 2-tuple linguistic Choquet averaging operator, Shapley 2-tuple linguistic Choquet geometric operator and generalized Shapley 2-tuple linguistic Choquet averaging operator. Then we discuss some properties of these operators, such as idempotency, monotonicity, boundary and commutativity. Secondly, if the information about the weights of decision makers (DMs) and attributes is incompletely known, we build two models to determine the optimal fuzzy measures on DM set and attribute set, respectively. Furthermore, we develop a new method for multiple attribute group decision making under 2-tuple linguistic environment based on the proposed operators. Finally, we apply the developed MAGDM method to select the most desirable emergency alternative and the validity of the developed method is verified by comparing the evaluation results with those obtained from the existing 2-tuple correlated aggregation operators.     

A group decision-making model based on incomplete comparative expressions with hesitant linguistic terms

As a result of uncertainty and complexity for environments of decision-making, it is more suitable for decision makers to use hesitant fuzzy linguistic information. In this paper, a novel group decision making (GDM) model based on fuzzy linear programming is proposed for incomplete comparative expressions with hesitant fuzzy linguistic term set (HFLTSs). We establish an equivalence theorem of additive consistency between 2-tuple fuzzy linguistic preference relation (FLPR) and corresponding fuzzy preference relation. Based on this framework, a fuzzy linear programming is established to address incomplete comparative expressions with HFLTSs. It is more important that the proposed fuzzy linear programming has a double action, finding the highest consistent incomplete 2-tuple FLPR and increasing inconsistent 2-tuple FLPR to the additive consistent 2-tuple FLPR based on given incomplete comparative expressions with HFLTSs. By this means, a novel GDM model is constructed based on importance induced ordered weighted averaging operator. Finally, an investment decision-making in real-world is solved by the proposed model, which shows the result of GDM is effectiveness.     

Partitioned Bonferroni mean based on linguistic 2-tuple for dealing with multi-attribute group decision making

In this study, a multi-attribute group decision making (MAGDM) problem is investigated, in which decision makers provide their preferences over alternatives by using linguistic 2-tuple. In the process of decision making, we introduce the idea of a specific structure in the attribute set. We assume that attributes are partitioned into several classes and members of intra-partition are interrelated while no interrelationship exists among inter partition. We emphasize the importance of having an aggregation operator, to capture the expressed inter-relationship structure among the attributes, which we will refer to as partition Bonferroni mean (PBM). We also investigate the behavior of the proposed PBM operator. Further to aggregate the given linguistic information to get overall performance value of each alternative in MAGDM, we analyze PBM operator in linguistic 2-tuple environment and develop three new linguistic aggregation operators: 2-tuple linguistic PBM (2TLPBM), weighted 2-tuple linguistic PBM (W2TLPBM) and linguistic weighted 2-tuple linguistic PBM (LW-2TLPBM). Based on the idea that total linguistic deviation between individual decision maker's opinions and group opinion should be minimized, we develop an approach to determine weight of the decision makers. Finally, a practical example is presented to illustrate the proposed method and comparison analysis demonstrates applicability of the proposed method.     

Optimal Narrowing of a Block of Sortings in Optimal Time

Let D be a totally ordered set. Call an n -block, a Cartesian product of n closed and possibly empty intervals of D. Let sort be the set of all 2n -tuples of elements of D of the form (x₁,...,x_2n) , where (x_n+1,...,x_2n) is the n -tuple obtained by sorting the elements of the n -tuple (x₁,...,x_n) in non-decreasing order. We present and justify an algorithm of complexity O(n log n) which, given a 2n -block a , computes a 2n -block which, by inclusion, is the smallest block containing the set sort a . We show that this complexity is optimal.     

A novel method for hybrid multiple attribute decision making

An approach based on 2-tuple is presented to solve the hybrid multiple attribute decision making problem with weight information unknown. First, transformation rules between linguistic variables and triangular fuzzy numbers, and distance between 2-tuple linguistics are defined, then the transformation method between 2-tuple linguistic and different forms of indicator values is given. Besides, according to grey incidence minimum deviation theory of positive ideal solution, the weights of indicators are determined, and then alternatives are ranked by 2-tuple linguistic weighting arithmetic average values. Finally, an illustrative example is given to demonstrate the procedure of the method and to compare with TOPSIS method to show the effectiveness and advantages of the presented method.     

On the k-tuple domination of de Bruijn and Kautz digraphs

In a digraph G, a vertex u is said to dominate itself and vertices v such that (u,v) is an arc of G. For a positive integer k, a k-tuple dominating set D of a digraph is a subset of vertices such that every vertex is dominated by at least k vertices in D. The k-tuple domination number of a given digraph is the minimum cardinality of a k-tuple dominating set of the digraph. In this letter, we give the exact values of the k-tuple domination number of de Bruijn and Kautz digraphs.     

一种基于二元语义的混合型多属性决策方法

针对指标权重未知的混合型多属性决策问题,提出一种基于二元语义的决策方法.首先,定义了语言评价变量与三角模糊数的转化规则和二元语义之间的距离,给出了不同类型指标数据与二元语义的转化;然后,利用与正理想解灰色关联度偏差最小原理,确定了属性的指标权重,并利用二元语义加权算术平均值对方案进行排序;最后,通过应用案例说明了所提方法的决策步骤,并与TOPSIS方法进行了比较,表明了所提方法的有效性和优越性.     

区间二元语义Bonferroni集成算子及其决策应用

区间二元语义值是一种常用的不确定环境下决策信息表达形式。考虑到决策信息的交叉影响作用,定义了区间二元语义值的Bonferroni平均算子以及相应的加权形式,在此基础上,给出了组合形式的区间二元语义值的加权Bonferroni平均算子的概念,并研究了算子的幂等性、单调性等数学性质,给出了基于C-I2TLWBA算子区间二元语义值的集成模型和决策应用。实例表明了该模型具有较好的有效性。