Rule acquisition of three-way semi-concept lattices in formal decision context

Three-way concept analysis is an important tool for information processing,and rule acquisition is one of the research hotspots of three-way concept analysis.However,compared with three-way concept lattices,three-way semi-concept lattices have three-way operators with weaker constraints,which can generate more concepts.In this article,the problem of rule acquisition for three-way semi-concept lattices is discussed in general.The authors construct the finer relation of three-way semi-concept lattices,and propose a method of rule acquisition for three-way semi-concept lattices.The authors also discuss the set of decision rules and the relationships of decision rules among object-induced three-way semi-concept lattices,object-induced three-way concept lattices,classical concept lattices and semi-concept lattices.Finally,examples are provided to illustrate the validity of our conclusions.

Realization of Rough Set Approximation Toplogical Operations Based on Formal Concept Analysis

There is an intimate correlation between rough set theory and formal concept analysis theory, so rough set approximations can be realized by means of formal concept analysis. For any given multiple valued information system, the realization of rough set approximation operation has two major steps, firstly convert the information system from multiple valued one to single valued formal context, secondly realize rough set approximation operations aided by concept lattice, which is equivalent to a query operation under some necessary conditions.

基于Concept-Ontology的联通分析与算法设计

在建立知识系统过程中,知识的联通分析是一个十分重要的内容。论文首先讨论了概念本体的设计思想以及概念本体的基本性质,然后分析了基于Concept-Ontology的概念联通方法以及基本性质,最后给出了概念联通的联通算法。

Role based access control design using Triadic concept analysis

Role based access control is one of the widely used access control models.There are investigations in the literature that use knowledge representation mechanisms such as formal concept analysis(FCA),description logics,and Ontology for representing access control mechanism.However,while using FCA,investigations reported in the literature so far work on the logic that transforms the three dimensional access control matrix into dyadic formal contexts.This transformation is mainly to derive the formal concepts,lattice structure and implications to represent role hierarchy and constraints of RBAC.In this work,we propose a methodology that models RBAC using triadic FCA without transforming the triadic access control matrix into dyadic formal contexts.Our discussion is on two lines of inquiry.We present how triadic FCA can provide a suitable representation of RBAC policy and we demonstrate how this representation follows role hierarchy and constraints of RBAC on sample healthcare network available in the literature.

Identification and Prediction of Interdisciplinary Research Topics: A Study Based on the Concept Lattice Theory

Purpose: Formal concept analysis(FCA) and concept lattice theory(CLT) are introduced for constructing a network of IDR topics and for evaluating their effectiveness for knowledge structure exploration.Design/methodology/approach: We introduced the theory and applications of FCA and CLT, and then proposed a method for interdisciplinary knowledge discovery based on CLT. As an example of empirical analysis, interdisciplinary research(IDR) topics in Information & Library Science(LIS) and Medical Informatics, and in LIS and Geography-Physical, were utilized as empirical fields. Subsequently, we carried out a comparative analysis with two other IDR topic recognition methods.Findings: The CLT approach is suitable for IDR topic identification and predictions.Research limitations: IDR topic recognition based on the CLT is not sensitive to the interdisciplinarity of topic terms, since the data can only reflect whether there is a relationship between the discipline and the topic terms. Moreover, the CLT cannot clearly represent a large amounts of concepts.Practical implications: A deeper understanding of the IDR topics was obtained as the structural and hierarchical relationships between them were identified, which can help to get more precise identification and prediction to IDR topics.Originality/value: IDR topics identification based on CLT have performed well and this theory has several advantages for identifying and predicting IDR topics. First, in a concept lattice, there is a partial order relation between interconnected nodes, and consequently, a complete concept lattice can present hierarchical properties. Second, clustering analysis of IDR topics based on concept lattices can yield clusters that highlight the essential knowledge features and help display the semantic relationship between different IDR topics. Furthermore, the Hasse diagram automatically displays all the IDR topics associated with the different disciplines, thus forming clusters of specific concepts and visually retaining and presenting the associations of IDR topics through multiple inheritance relationships between the concepts.

Construction and application of formal ontology for mine

Digital mine is the only way for the development of mining industry in China. Due to lack of appropriate standards and norms, and different awareness in the field of digital mine among academia and industry insiders, the meaning for digital mine is still unclear. Starting from the nature of mining and removing of views of specialized fields, this paper constructs formal ontology for digital mine and proposes the four levels for it. The ontology clarifies the concept world for digital mine, defines the meaning of concepts and relations clearly, provides a reference for the standard construction for digital mine and provides a unified semantic framework for the integration of heterogeneous mine data. Meanwhile, it can provide formal reasoning knowledge for expert system of digital mine and improve the intelligence and automation while the machine automatically interpreting and processing mine spatial data.

Exploring the relationship between rarity and price of profile picture NFT:A formal concept analysis on the BAYC NFT collection

Non-fungible token(NFT)is a digital asset whose ownership can be validated and controlled via blockchain technology.The NFT market is a rapidly growing field,and the rarity of NFT is an essential factor that affects its price,as scarcity leads to higher demand.This study focuses on the BAYC NFT collection,which is a successful and representative collection of profile picture NFT,and analyzes how rarity affects NFT prices.This paper investigates the relationship between the rarity and price of the BAYC NFT collection using formal concept analysis(FCA)method.The results show that rarity is a major factor influencing the price of NFT and the effect is more apparent in the medium rarity range.When rarity is very high or very low,other factors become significant determinants,such as the uniqueness and appeal of NFT,and even the naturalness of NFT images.This research highlights the importance of considering rarity when assessing NFT and underscores the need for a comprehensive evaluation of NFT rarity.This study also provides valuable insights into the NFT market and can be useful for NFT investors,creators,and collectors.Furthermore,the usefulness of FCA as a tool for quantifying NFT rarity and evaluating NFT price was demonstrated.

Attribute reduction theory of concept lattice based on decision formal contexts

The theory of concept lattices is an efficient tool for knowledge representation and knowledge discovery, and is applied to many fields successfully. One focus of knowledge discovery is knowledge reduction. Based on the reduction theory of classical formal context, this paper proposes the definition of decision formal context and its reduction theory, which extends the reduction theory of concept lattices. In this paper, strong consistence and weak consistence of decision formal context are defined respectively. For strongly consistent decision formal context, the judgment theorems of consistent sets are examined, and approaches to reduction are given. For weakly consistent decision formal context, implication mapping is defined, and its reduction is studied. Finally, the relation between reducts of weakly consistent decision formal context and reducts of implication mapping is discussed.

A fuzzy formal concept analysis based approach for business component identification

Identifying business components is the basis of component-based software engineering. Many approaches, including cluster analysis and concept analysis, have been proposed to identify components from business models. These approaches classify business elements into a set of components by analyzing their properties. However, most of them do not consider the difference in their properties for the business elements, which may decrease the ac- curacy of the identification results. Fhrthermore, component identification by partitioning business elements cannot reflect which features are responsible for the generation of certain results. This paper deals with a new approach for component identification from business models using fuzzy formal concept analysis. First, the membership between business elements and their properties is quantified and transformed into a fuzzy formal context, from which the concept lattice is built using a refined incremental algorithm. Then the components are selected from the concepts according to the concept dispersion and distance. Finally, the effectiveness and efficiency are validated by applying our approach in the real-life cases and experiments.

Automatically Constructing an Effective Domain Ontology for Document Classification

An effective domain ontology automatically constructed is proposed in this paper. The main concept is using the Formal Concept Analysis to automatically establish domain ontology. Finally, the ontology is acted as the base for the Naive Bayes classifier to approve the effectiveness of the domain ontology for document classification. The 1752 documents divided into 10 categories are used to assess the effectiveness of the ontology, where 1252 and 500 documents are the training and testing documents, respectively. The Fl-measure is as the assessment criteria and the following three results are obtained. The average recall of Naive Bayes classifier is 0.94. Therefore, in recall, the performance of Naive Bayes classifier is excellent based on the automatically constructed ontology. The average precision of Naive Bayes classifier is 0.81. Therefore, in precision, the performance of Naive Bayes classifier is gored based on the automatically constructed ontology. The average Fl-measure for 10 categories by Naive Bayes classifier is 0.86. Therefore, the performance of Naive Bayes classifier is effective based on the automatically constructed ontology in the point of F 1-measure. Thus, the domain ontology automatically constructed could indeed be acted as the document categories to reach the effectiveness for document classification.

Study of Decision Implications Based on Formal Concept Analysis

Serve to introduce decision context and decision implication to Formal Concept Analysis （FCA）. Since extracting decision implications directly from decision context takes time, we present an inference rule to reduce the number of decision implications. Moreover, based on the inference rule we introduce the notion of a-maximal decision implication and prove that the set of all α-maximal decision implications is α-complete and α-non-redundant. Finally, we propose a method to generate the set.

Skyline refinement exploiting fuzzy formal concept analysis

Purpose-The study of the skyline queries has received considerable attention from several database researchers since the end of 2000’s.Skyline queries are an appropriate tool that can help users to make intelligent decisions in the presence of multidimensional data when different,and often contradictory criteria are to be taken into account.Based on the concept of Pareto dominance,the skyline process extracts the most interesting(not dominated in the sense of Pareto)objects from a set of data.Skyline computation methods often lead to a set with a large size which is less informative for the end users and not easy to be exploited.The purpose of this paper is to tackle this problem,known as the large size skyline problem,and propose a solution to deal with it by applying an appropriate refining process.Design/methodology/approach-The problem of the skyline refinement is formalized in the fuzzy formal concept analysis setting.Then,an ideal fuzzy formal concept is computed in the sense of some particular defined criteria.By leveraging the elements of this ideal concept,one can reduce the size of the computed Skyline.Findings-An appropriate and rational solution is discussed for the problem of interest.Then,a tool,named SkyRef,is developed.Rich experiments are done using this tool on both synthetic and real datasets.Research limitations/implications-The authors have conducted experiments on synthetic and some real datasets to show the effectiveness of the proposed approaches.However,thorough experiments on large-scale real datasets are highly desirable to show the behavior of the tool with respect to the performance and time execution criteria.Practical implications-The tool developed SkyRef can have many domains applications that require decision-making,personalized recommendation and where the size of skyline has to be reduced.In particular,SkyRef can be used in several real-world applications such as economic,security,medicine and services.Social implications-This work can be expected in all domains that require decision-making like hotel finder,restaurant recommender,recruitment of candidates,etc.Originality/value-This study mixes two research fields artificial intelligence(i.e.formal concept analysis)and databases(i.e.skyline queries).The key elements of the solution proposed for the skyline refinement problem are borrowed from the fuzzy formal concept analysis which makes it clearer and rational,semantically speaking.On the other hand,this study opens the door for using the formal concept analysis and its extensions in solving other issues related to skyline queries,such as relaxation.

面向知识结构分析的模糊概念格模型

知识空间理论使用数学语言对学习者进行知识评价与学习指导,属于数学心理学的研究范畴.技能与问题是构成知识空间的两个基本要素,深入研究两者之间的关系是知识状态刻画与知识结构分析的内在要求.在当前的知识空间理论研究中,没有明确建立技能与问题之间的双向映射,从而难以提出直观概念意义下的知识结构分析模型,也没有明确建立知识状态之间的偏序关系,不利于刻画知识状态之间的差异,更不利于规划学习者未来的学习路径.此外,现有的成果主要集中在经典的知识空间,没有考虑实际问题中数据的不确定性.为此,将形式概念分析与模糊集引入知识空间理论,建立面向知识结构分析的模糊概念格模型.具体地,分别建立知识空间与闭包空间的模糊概念格模型.首先,建立知识空间模糊概念格,并通过任意两个概念的上确界证明所有概念的外延构成知识空间.引入粒描述的思想定义技能诱导的问题原子粒,由问题原子粒的组合判定一个问题组合是否是知识空间中的一个状态,进而提出由问题组合获取知识空间模糊概念的方法.其次,建立闭包空间模糊概念格,并通过任意两个概念的下确界证明所有概念的外延构成闭包空间.类似地,定义问题诱导的技能原子粒,由技能原子粒的组合判定一个技能组合是否是闭包空间中某一知识状态所需的技能,进而提出由技能组合获取闭包空间模糊概念的方法.最后,通过实验分析问题数量、技能数量、填充因子以及分析尺度对知识空间与闭包空间规模的影响.结论表明知识空间模糊概念不同于现有的任何概念,也不能从其他概念派生而来.闭包空间模糊概念本质上是一种面向属性单边模糊概念.在二值技能形式背景中,知识空间与闭包空间中的状态具有一一对应关系,但这种关系在模糊技能形式背景中并不成立.

三支区间集半概念的代数结构及覆盖粗糙近似算子

针对在一个形式背景中以区间集为底集,考虑一个属性集(对象集)拥有的对象集(属性集)和不拥有的对象集(属性集)的知识表述而进行知识提取的问题,采取将区间集概念与三支决策、经典半概念相结合的方法,产生AE-区间集半概念和OE-区间集半概念两种形式的三支区间集半概念,同时发现AE-区间集半概念与OE-区间集半概念的纯双布尔代数结构。进一步深入讨论可知,AE-区间集半概念可分为AE1-区间集半概念与AE2-区间集半概念,利用粗糙集理论分别挖掘与AE1-区间集半概念和AE2-区间集半概念有关的近似算子的结构性质,对偶地可得OE-区间集半概念的相关结果。所得三支区间集半概念拓广了已有的三支决策集分别与区间集概念和半概念相结合的相关成果,成为一个新的知识表述。

决策形式背景基于OE-协调性的属性约简

属性约简作为形式概念分析中非常重要的一个研究分支,在三支概念分析中也同样重要。基于对象导出三支概念格,提出了保持决策形式背景OE-协调性的属性约简理论,丰富了三支概念分析的约简理论。首先,定义了决策形式背景的OE-协调集和OE-约简,并将属性按其特征分为3类。其次,指出OE-约简的本质就是极小OE-协调集,给出了OE-协调集的几个判定定理,通过研究OE-协调集的充要条件,获取OE-约简的判定定理。最后,给出OE-差别矩阵和OE-差别函数的定义,并给出了利用OE-差别矩阵和OE-差别函数计算OE-约简的方法。

知识空间理论综述

知识空间理论是一种研究教育规律的科学方法,已取得一系列研究成果.文中旨在全面综述知识空间理论的研究工作.首先,阐述构建知识结构的方法和原则,介绍良级性的研究内容,并强调其在知识空间理论研究中的重要性,归纳总结推测关系的相关工作,并介绍问题之间、项目之间推测关系的研究方法.然后,分别从技能映射、技能函数、能力-绩效方法三方面梳理基于能力的知识空间理论的研究进展.进一步地,概述知识空间理论与概率模型、粒计算等结合的研究现状,并介绍知识空间理论在辅助学习与自适应测试方面的应用.最后,探讨上述研究中存在的关键科学问题,并提出初步的研究思路,为该领域的后续研究提供有益的参考.

一种多线程概念约简算法

针对现有概念约简算法计算过程较为繁琐且执行效率低的问题,提出了一种多线程概念约简算法MTCR。MTCR以提高计算概念约简的效率为首要目标,在多核环境下利用多线程技术并行计算概念约简。首先,MTCR算法使用两个线程分别计算单个对象的对象代表概念集和单个属性的属性代表概念集;然后,将形式背景中的对象(属性)依次放入p个队列,并为每个队列创建线程;最后,通过多线程方式并行计算任意对象的对象代表概念集和任意属性的属性代表概念集,以及两类代表概念集的交集,进而构建代表概念矩阵,据此计算出所有概念约简。在MTCR算法中,使用多线程的每个阶段的数据相对独立,使得多线程之间不需要频繁的同步操作,从而减少了线程之间的竞争和等待。这样可充分有效地利用计算资源,大大提升算法的性能。UCI数据集和随机数据集上的实验表明:MTCR算法可以准确得到概念约简结果,在使用单线程情况下执行速度与串行概念约简算法SCR相近;当线程数不超过8时,线程数每增加1倍,MTCR算法执行速度可提高30%以上。

面向属性概念格下的知识状态转移方法

如何高效率地寻找猜测答对或粗心答错情况下不相容答题状态对应受测者真实的知识状态是目前计算机自适应测试领域研究的一个热点问题.现有知识状态转移方法时间成本高,不适用于含有大量测试问题和技能的应用场景.并且,现有知识状态转移方法将合取模型和能力模型均视为能力模型,采用同一种方法进行知识状态转移,灵活性不够,评估效率不高.本文针对合取模型和能力模型,分别提出基于面向属性概念格的知识状态转移方法.首先由技能映射或多映射建立技能背景并诱导出对应的面向属性概念格,进一步使用概念格中概念的外延并结合最大概率方法得到受测者猜测或粗心情况下的真实知识状态,最后给出知识评估过程.实验表明,在知识评估结果相同的前提下,本文所提方法相比现有方法极大地降低了评估时间成本,因此具有更好的性能.

保持决策蕴涵不变的决策背景属性约简

形式概念分析是一种利用概念格进行数据分析的理论,属性约简是概念格约简的主要方式之一。决策蕴涵是形式概念分析在决策情形下的一种知识表示与推理模型。在已有保持决策背景知识信息不变的属性约简研究中,通常以保持概念规则或粒规则来保持决策背景的知识信息。而相比于概念规则与粒规则,决策蕴涵具备更强的知识表示能力。为了进一步缩小数据在属性约简前后对知识信息表示的差异,对保持决策蕴涵不变的属性约简进行了研究。首先,结合决策蕴涵的语义给出了保持决策蕴涵不变的协调集和约简定义,提出了判定协调集和约简的充要条件;接着,通过实例分析了该约简存在的问题,并结合蕴涵理论给出解决方法,从而给出了弱协调集和弱约简的定义;然后,从知识包含的角度分析了弱约简相比于约简的合理性;最后,提出了判定弱协调集和弱约简的充要条件,并结合决策蕴涵规范基给出了能够找到弱约简的方法,丰富了保持知识信息的属性约简研究内容。

基于对象阈值变精度概念的启发式推荐方法

针对启发式概念推荐方法进行优化,提出一种基于对象阈值变精度概念的启发式推荐方法。将模糊形式背景转化为对象阈值可变的变精度形式背景,在此形式背景的基础上定义概念构造的启发式信息;利用内涵约束,在保证群组相似度的基础上,构造当前加权面积最大的概念,将这些概念组成强概念集合;在这个概念集合中利用组推荐方法对所有用户进行推荐。实验在MovieLens系列数据集和FilmTrust数据集上的一系列结果验证这种优化是有效的,能够大幅加强推荐的精度和性能。