Generating Sets of the Complete Semigroup of Binary Relations Defined by Semilattices of the Class Σ8(X, 5)

In this article, we study generating sets of the complete semigroups of binary relations defined by X-semilattices of unions of the class Σ8(X, 5). Found uniquely irreducible generating set for the given semigroups and when X is finite set formulas for calculating the number of elements in generating sets are derived.

Regular Elements of the Complete Semigroups <i>B_X(D)</i>of Binary Relations of the Class &sum;₂(<i>X</i>,8)

As we know if D is a complete X-semilattice of unions then semigroup Bx(D) possesses a right unit iff D is an XI-semilattice of unions. The investigation of those a-idempotent and regular elements of semigroups Bx(D) requires an investigation of XI-subsemilattices of semilattice D for which V(D,a)=Q∈∑2(X,8) . Because the semilattice Q of the class ∑2(X,8) are not always XI -semilattices, there is a need of full description for those idempotent and regular elements when V(D,a)=Q . For the case where X is a finite set we derive formulas by calculating the numbers of such regular elements and right units for which V(D,a)=Q .

Generating Set of the Complete Semigroups of Binary Relations

Difficulties encountered in studying generators of semigroup of binary relations defined by a complete X -semilattice of unions D arise because of the fact that they are not regular as a rule, which makes their investigation problematic. In this work, for special D, it has been seen that the semigroup , which are defined by semilattice D, can be generated by the set .

Picture Fuzzy Relations over Picture Fuzzy Sets

Nowadays, picture fuzzy set theory is a flourishing field in mathematics with uncertainty by incorporating the concept of positive, negative and neutral membership degrees of an object. A traditional crisp relation represents the satisfaction or the dissatisfaction of relationship, connection or correspondence between the objects of two or more sets. However, there are some problems that can’t be solved through classical relationships, such as the relationship between two objects being vague. In those situations, picture fuzzy relation over picture fuzzy sets is an important and powerful concept which is suitable for describing correspondences between two vague objects. It represents the strength of association of the elements of picture fuzzy sets. It plays an important role in picture fuzzy modeling, inference and control system and also has important applications in relational databases, approximate reasoning, preference modeling, medical diagnosis, etc. In this article, we define picture fuzzy relations over picture fuzzy sets, including some other fundamental definitions with illustrations. The max-min and min-max compositions of picture fuzzy relations are defined in the light of picture fuzzy sets and discussed some properties related to them. The reflexivity, symmetry and transitivity of a picture fuzzy relation are described over a picture fuzzy set. Finally, various properties are explored related to the picture fuzzy relations over a picture fuzzy set.

Ni-Ga BINARY PHASE RELATIONS AT 700℃

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Generated Sets of the Complete Semigroup Binary Relations Defined by Semilattices of the Class Σ₈(<em>X</em>, <em>n</em>+ <em>k</em>+ 1)

In this article, we study generated sets of the complete semigroups of binary relations defined by X-semilattices unions of the class Σ8 (X, n + k +1) , and find uniquely irreducible generating set for the given semigroups.

On Granularity in Information Systems Based on Binary Relation

In this paper, some important issues of granularity are discussed mainly in information systems (ISs) based on binary relation. Firstly, the vector representation method of knowledge granules is proposed in an infor-mation system based on binary relation to eliminate limitations of set representation method. Secondly, operators among knowledge granularity are introduced and some important properties of them are studied carefully. Thirdly, distance between two knowledge granules is established and granular space is constructed based on it. Fourthly, axiomatic definition of knowledge granularity is investigated, and one can find that some existed knowledge granularities are special cases under the definition. In addition, as an application of knowledge granular space, an example is employed to validate some results in our work.

On Enforcing Dyadic-type Homogeneous Binary Function Product Constraints in MatBase

Homogeneous binary function products are frequently encountered in the sub-universes modeled by databases,spanning from genealogical trees and sports to education and healthcare,etc.Their properties must be discovered and enforced by the software applications managing such data to guarantee plausibility.The(Elementary)Mathematical Data Model provides 17 types of dyadic-based homogeneous binary function product constraint categories.MatBase,an intelligent data and knowledge base management system prototype,allows database designers to simply declare them by only clicking corresponding checkboxes and automatically generates code for enforcing them.This paper describes the algorithms that MatBase uses for enforcing all 17 types of homogeneous binary function product constraint,which may also be employed by developers without access to MatBase.

A Fast Distributed Algorithm for Association Rule Mining Based on Binary Coding Mapping Relation

Association rule mining is an important issue in data mining. The paper proposed an binary system based method to generate candidate frequent itemsets and corresponding supporting counts efficiently, which needs only some operations such as ＂and＂, ＂or＂ and ＂xor＂. Applying this idea in the existed distributed association rule mining al gorithm FDM, the improved algorithm BFDM is proposed. The theoretical analysis and experiment testify that BFDM is effective and efficient.

Generating Sets of the Complete Semigroups of Binary Relations Defined by Semilattices of the Class Σ_(2)(X,4)

In this paper, we have studied generating sets of the complete semigroups defined by X-semilattices of the class Σ2(X, 4).

Complete Semigroups of Binary Relations Defined by Semilattices of the Class Σ_(1)(X,10)

In this paper we give a full description of idempotent elements of the semigroup BX (D), which are defined by semilattices of the class ∑1 (X, 10). For the case where X is a finite set we derive formulas by means of which we can calculate the numbers of idempotent elements of the respective semigroup.

Idempotent and Regular Elements of the Complete Semigroups of Binary Relations of the Class Σ_(3)(X,9)

In this paper, we take Q16 subsemilattice of D and we will calculate the number of right unit, idempotent and regular elements α of BX (Q16) satisfied that V (D, α) = Q16 for a finite set X. Also we will give a formula for calculate idempotent and regular elements of BX (Q) defined by an X-semilattice of unions D.

Binary Relations between Magnitudes of Different Dimensions Used in Material Science Optimization Problems Pseudo-State Equation of Soft Magnetic Composites

New algorithm for optimizing technological parameters of soft magnetic composites has been derived on the base of topological structure of the power loss characteristics. In optimization magnitudes obeying scaling, it happens that one has to consider binary relations between the magnitudes having different dimensions. From mathematical point of view, in general case such a procedure is not permissible. However, in a case of the system obeying the scaling law it is so. It has been shown that in such systems, the binary relations of magnitudes of different dimensions is correct and has mathematical meaning which is important for practical use of scaling in optimization processes. The derived structure of the set of all power loss characteristics in soft magnetic composite enables us to derive a formal pseudo-state equation of Soft Magnetic Composites. This equation constitutes a relation of the hardening temperature, the compaction pressure and a parameter characterizing the power loss characteristic. Finally, the pseudo-state equation improves the algorithm for designing the best values of technological parameters.

Relational Representations of Strongly Algebraic Lattices

In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.

基于潜在关系的实体关系联合抽取模型

实体关系联合抽取的作用是从特定文本中识别出实体和对应关系,同时它也是知识图谱构建和更新的基础。目前的联合抽取方法在追求性能的同时都忽略了抽取过程中的信息冗余。针对此问题,提出基于潜在关系的实体关系联合抽取模型,通过设计一种新的解码方式来减少预测过程中关系、实体和三元组的冗余信息,从整体上分为提取潜在实体对、解码关系两步来完成从句子中抽取三元组的任务。首先通过潜在实体对提取器预测实体间是否存在潜在关系,同时筛选出置信度高的实体对作为最终的潜在实体对;其次将关系解码视作多标签二分类任务,通过关系解码器预测每个潜在实体对之间全部关系的置信度;最后通过置信度确定关系数量和类型,以完成三元组的抽取任务。在两个通用数据集上的实验结果表明,所提模型相比基线模型在准确率和F1指标上的效果更好,验证了所提模型的有效性,消融实验也证明了模型内部各部分的有效性。

风险投资机构二元关系的演变及其退出效应研究

基于中国风投市场2004—2018年的投资事件数据和2004—2021年的退出数据,构建风险投资机构成对的数据集,研究风险投资二元关系演变的影响因素,进而探讨其对退出的影响。研究发现,风投机构间的匹配度、网络位置、历史联合投资行为对其二元关系产生显著的正面影响,而风投机构的间接合作伙伴会对此有显著的负面影响。进一步分析发现,风投机构匹配度越高、网络位置越中心、历史联合投资行为越多,其退出的可能性越小。研究结论对风险投资机构如何选择合作伙伴有一定的借鉴意义。

基于一般二元关系粗糙近似算子的格结构研究

刻画了基于一般二元关系及悲观多粒度粗糙近似算子的完备格结构,证明了在选取蕴涵算子之后,基于一般二元关系的粗糙近似算子构成MV、R0与布尔代数。

二元模糊关系范畴的对称幺半范畴性

结合模糊关系范畴的概念给出了二元模糊关系范畴L_(b)Rel的概念.首先,讨论了范畴L_(b)Rel的积和余积的结构.其次,定义了张量积函子■,得到了L_(b)Rel是对称幺半范畴.进而,给出了范畴L_(b)Rel中的幺半群和余幺半群结构.最后,以二元模糊关系范畴L_(b)Rel作为纽带,构造了一个从模糊集范畴LSet到模糊关系范畴RelLL的忠实函子.

面向属性概念格的概念特征与概念约简

提出面向属性概念协调集和概念约简,定义了包含补二元关系的面向属性概念极小集,讨论了面向属性概念格中核心概念、相对必要概念及不必要概念的概念特征,并研究了三种概念的判别方法.给出了面向属性概念约简的可行方法及其相应算法.

基于二元语义GRP法的应急资源动员合作模式选择方法

为对应急资源动员合作模式的选择提供量化依据,建立了应急资源动员中地方政府合作的“介入—强度—方式”三维结构模型,从中选取4种典型合作模式,将模式选择问题转化为具有语言评价信息的多指标群决策问题。采用基于二元语义灰色关联投影的信息处理群决策方法,构建了合作模式的选择模型。依据传统投影分析方法的基本思想,通过计算备选方案对正理想方案和负理想方案的投影值,得到备选方案对正理想方案的相对贴近度,最终确定最优方案。在理论研究基础上,对京津冀地区应急资源动员合作模式进行实证分析,发现京津冀地区的应急资源动员合作更适合采取上级政府介入的强行政合作模式。基于专家评价数据的算例结果表明,该方法能够较好地反映合作模式与客观情况的匹配程度,在模式选择中发挥较好的作用。