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.

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.

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.

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.

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.

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.

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.

单边区间集模糊半概念的知识表示及提取方法

为了使“区间”形式加以表述的不确定信息的提取具有侧重性,需提取出对象(属性)集对应的属性(对象)区间集。本文在模糊形式背景中,通过引入2个阈值,将单边区间集与经典半概念结合,提取出属性(对象)集对应的对象(属性)区间集,从而提出区间集外延–集合内涵(集合外延–区间集内涵)(interval set extent-set intent(set extent-interval set intent),ISE-SI(SE-ISI))型单边区间集模糊半概念。全体ISE-SI(SE-ISI)型单边区间集模糊半概念构成格,并给出基于格搜寻全体ISE-SI(SE-ISI)型单边区间集模糊半概念的算法。通过与已有成果对比,显示出这2种知识表示形式的多方优势。本文所得结果在知识表示及提取方法上具有适用范围广、实际应用强等优点。

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。

属性偏序形式结构的数学形式化

属性偏序形式结构,作为一种基于人类认知原理和粒计算思想的知识发现和知识表示新理论,目前已有广泛的应用,但其理论基础缺乏抽象化数学化,这势必影响该理论的系统发展。针对上述问题,研究了属性偏序形式结构的数学形式化描述问题。首先,基于粒计算的思想提出了知识表示的形式化框架。在此基础上,通过定义对象集合的覆盖和最简覆盖,给出属性偏序形式结构的粒和粒群的概念,进而通过对粒衍生出粒群的充要条件的讨论,给出了属性偏序形式结构中的知识结构,从而完成属性偏序形式结构的数学形式化描述。最后,通过具体实例展示了利用数学形式化描述构造属性偏序形式结构的过程,并揭示了该过程所体现的人类认知规律。

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.

形式背景上近似推理生成决策蕴涵研究

基于形式背景获取决策蕴涵、概念规则等知识是数据分析、机器学习的重要研究内容之一.首先,利用属性逻辑语义对决策蕴涵的特性进行刻画.其次,在经典二值逻辑框架下分析决策蕴涵、概念规则的基于全蕴涵三I推理思想及分离规则(Modus ponens,MP)和逆分离规则(Modus tonens,MT)的近似推理模式的特征,证明决策蕴涵的MP、MT近似推理结论是决策蕴涵,概念规则的MP、MT近似推理结论是概念规则等结论.引进属性逻辑公式的伪距离,在属性逻辑伪距离空间中分析推理对象范围参数变化对决策蕴涵MP、MT近似推理结论的影响.最后,提出若干通过MP、MT近似推理生成决策蕴涵、概念规则及拟决策蕴涵的模式和方法,数值实验验证了所提方法的有效性.

基于待选集的三元概念构造方法

三元概念分析作为形式概念分析理论的扩展,是一种分析三维数据的理论.获取三元概念是三元概念分析理论的重要问题之一,文中提出基于待选集的三元概念构造方法.首先,定义正则三元背景和净化三元背景,研究这两种三元背景的性质,证明三元背景诱导的形式背景的所有形式概念的外延集包含三元背景所有三元概念的外延集.然后,定义外延待选集,给出利用外延待选集构造三元概念的方法,加快获取三元概念的速度.进一步,证明依据该构造方法获取三元概念的可行性和完备性,同时将该构造方法推广到三元背景诱导的另两种形式背景上.最后,给出基于待选集的三元概念构造算法,并通过实验验证文中算法性能较优.

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。

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。

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.

基于背景间运算的部分已知概念构造

概念是利用形式概念分析进行知识获取的基础。在不完备形式背景中,为了表达“一定具有”以及“可能具有”的关系,概念的外延或内涵通常以区间集的形式表达,称这样的概念为部分已知概念。由部分已知概念的定义可知,其本质与不完备背景的最小和最大完备化有关,因而考虑对最小和最大完备化背景进行运算来寻找部分已知概念。通过将不完备形式背景的最小完备化与最大完备化分别进行并置和叠置构造两个新背景,其概念格分别同构于SE-ISI概念格和ISE-SI概念格,从而提出了构建SE-ISI概念格和ISE-SI概念格的新方法。对于ISE-ISI概念,使用不完备形式背景的最小与最大完备化的直和运算构造了新的形式背景,基于此背景提出了寻找ISE-ISI概念的方法。

基于异构网络语言形式背景的知识发现及规则提取

在不确定性环境下,如何处理具有复杂关系的数据是研究热点之一.网络形式背景将复杂网络分析和形式概念分析结合,为复杂关系数据的知识发现提供一种有效的数学工具.文中首先从网络结构的异构性出发,提出异构网络语言形式背景.异构网络包含专家给出的主观网络,又包含通过对象的特征挖掘的客观网络.然后,考虑网络的连通性,得到全局和局部异构网络语言概念,并给出异构网络下的全局连通及局部连通知识发现算法.最后,基于异构网络语言形式背景构建关联规则提取模型,通过实例验证知识发现及规则提取的合理性和有效性.