Variable threshold concept lattices

In this paper, the definition of a variable threshold concept lattice is introduced. Based on a Galois connection, three kinds of variable threshold concept lattices, in which diverse requirements of knowledge discovery can be satisfied by adjusting a threshold, are defined. The number of formal concepts in a variable threshold concept lattice is far less than that in a fuzzy concept lattice. The three kinds of variable threshold concept lattices are constructed between two crisp sets, between a crisp set and a fuzzy set, and between a fuzzy set and a crisp set. Their properties are analogous to that of the classical concept lattices, and can be induced by the fuzzy concept lattice.     

On basic conditions to generate multi-adjoint concept lattices via Galois connections

This paper introduces sufficient and necessary conditions with respect to the fuzzy operators considered in a multi-adjoint frame under which the standard combinations of multi-adjoint sufficiency, possibility, and necessity operators form (antitone or isotone) Galois connections. The underlying idea is to study the minimal algebraic requirements so that the concept-forming operators (defined using the same syntactical form than the extension and intension operators of multi-adjoint concept lattices) form a Galois connection. As a consequence, given a relational database, we have much more possibilities to construct concept lattices associated with it, so that we can choose the specific version which better suits the situation.     

A local approach to concept generation

Generating concepts defined by a binary relation between a set of properties and a set of objects is one of the important current problems encountered in Data Mining and Knowledge Discovery in Databases. We present a new algorithmic process which computes all the concepts, without requiring an exponential-size data structure, and with a good worst-time complexity analysis, which makes it competitive with the best existing algorithms for this problem. Our algorithm can be used to compute the edges of the lattice as well at no extra cost.      

Isotone fuzzy Galois connections with hedges

We study isotone fuzzy Galois connections and concept lattices parameterized by particular unary operators. The operators represent linguistic hedges such as “very”, “rather”, “more or less”, etc. Isotone fuzzy Galois connections and concept lattices provide an alternative to their antitone counterparts which are the fundamental structures behind formal concept analysis of data with fuzzy attributes. We show that hedges enable us to control the number of formal concepts in the associated concept lattice. We also describe the structure of the concept lattice and provide a counterpoint to the main theorem of concept lattices.     

A new algebraic structure for formal concept analysis

Formal concept analysis (FCA) originally proposed by Wille [39], is an important theory for data analysis and knowledge discovery. Concept lattice is the core of the mathematical theory of formal concept analysis. To address the requirements of real word applications, concept lattice has been extended to many other forms from the theoretical point of view and possible applications. In this paper, with the aim of deriving the mathematical properties of formal concepts from the point of algebra, we propose a new algebra system for the formal context. Under the frame of the proposed system, some interesting properties of formal concepts are explored, which could be applied to explore concept hierarchy and ontology merging.     

一种区间数分解与定标算法及其扩展形式背景的概念格生成方法

现有的概念格模型无法处理既包含以布尔值表示的信息,又包含以标量、模糊数及区间数表示的信息。因此,针对包含所有这些信息类型的扩展的形式背景提出它的处理方法,在此基础上,生成经扩展的概念格,是一项有意义的工作。提出了一种新的区间数分解与定标算法,以处理含有多种类型的扩展形式背景,并给出了相应的扩展格生成算法。最后,实验表明,该方法具有良好的效果。     

Evaluation of IPAQ questionnaires supported by formal concept analysis

The paper presents a method for evaluation of questionnaires supported by formal concept analysis. Formal concept analysis provides an expert with a structured view on the data contained in the questionnaires. The method results from experiments with IPAQ (International Physical Activity Questionnaire). The structured view on the data provided by the method suggests various hypotheses which can later be tested. In addition, the structured view on data itself proved to be sufficiently informative to the expert. In addition to the method, the paper presents experiments with evaluation of IPAQ.     

基于形式概念分析的词义理解研究

探讨了形式概念分析在自然语言理解中的多义词分析及义素分析中的应用。在对多义词进行分析时,根据词性与词义之间的二元关系,构造词性与词义的决策背景,进而发现了词性与词义之间的决策规则,并对这些决策规则进行了解释;在对义素分析进行研究时,根据语言对象及其语义特征之间的二元关系构造形式背景,并在此背景上分析语言对象,实例表明了形式概念分析既可以很容易地对词语进行分类,又可以很直观地反映词类之间的关系,是进行义素分析的一种有效工具。     

基于不相关属性集合的属性探索算法

作为形式概念分析理论中的一个重要工具,属性探索算法能够以问题为导向,交互式地逐步发现系统知识,在知识的发现和获取中居于核心地位.但是,当形式背景的规模较大时,属性探索算法的计算过程过于耗时,严重制约了算法在当前大数据时代的推广与应用.耗时瓶颈主要存在于"寻找下一个与专家交互的问题"这一环节,传统算法在此过程中存在大量冗...     

Formal concept analysis in knowledge processing: A survey on applications

This is the second part of a large survey paper in which we analyze recent literature on Formal Concept Analysis (FCA) and some closely related disciplines using FCA. We collected 1072 papers published between 2003 and 2011 mentioning terms related to Formal Concept Analysis in the title, abstract and keywords. We developed a knowledge browsing environment to support our literature analysis process. We use the visualization capabilities of FCA to explore the literature, to discover and conceptually represent the main research topics in the FCA community. In this second part, we zoom in on and give an extensive overview of the papers published between 2003 and 2011 which applied FCA-based methods for knowledge discovery and ontology engineering in various application domains. These domains include software mining, web analytics, medicine, biology and chemistry data.     

From laser-scanned data to feature human model: a system based on fuzzy logic concept

This paper describes the development of a prototype system using fuzzy logic concept for constructing a feature human model, which is to be stored in a 3D digital human model database. In our approach, the feature human model is constructed by unorganized cloud points obtained from 3D laser scanners. Firstly, noisy points are removed, and the orientation of the human model is adjusted; secondly, a feature based mesh generation algorithm is applied on the cloud points to construct the mesh surface of a human model; lastly, semantic features of the human model are extracted from the mesh surface. Compared with earlier approach, our method strongly preserves the topology of a human model; more details can be constructed; and both the robustness and the efficiency of the algorithm are improved. At the end of the paper, in order to demonstrate the functionality of feature human models, potential applications are given.     

Formal Concept Analysis in knowledge processing: A survey on models and techniques

This is the first part of a large survey paper in which we analyze recent literature on Formal Concept Analysis (FCA) and some closely related disciplines using FCA. We collected 1072 papers published between 2003 and 2011 mentioning terms related to Formal Concept Analysis in the title, abstract and keywords. We developed a knowledge browsing environment to support our literature analysis process. We use the visualization capabilities of FCA to explore the literature, to discover and conceptually represent the main research topics in the FCA community. In this first part, we zoom in on and give an extensive overview of the papers published between 2003 and 2011 on developing FCA-based methods for knowledge processing. We also give an overview of the literature on FCA extensions such as pattern structures, logical concept analysis, relational concept analysis, power context families, fuzzy FCA, rough FCA, temporal and triadic concept analysis and discuss scalability issues.     

AVCD-FRA: A novel solution to automatic video cut detection using fuzzy-rule-based approach

Video shot boundary detection (SBD) is a fundamental step in automatic video content analysis toward video indexing, summarization and retrieval. Despite the beneficial previous works in the literature, reliable detection of video shots is still a challenging issue with many unsolved problems. In this paper, we focus on the problem of hard cut detection and propose an automatic algorithm in order to accurately determine abrupt transitions from video. We suggest a fuzzy rule-based scene cut identification approach in which a set of fuzzy rules are evaluated to detect cuts. The main advantage of the proposed method is that, we incorporate spatial and temporal features to describe video frames, and model cut situations according to temporal dependency of video frames as a set of fuzzy rules. Also, while existing cut detection algorithms are mainly threshold dependent; our method identifies cut transitions using a fuzzy logic which is more flexible. The proposed algorithm is evaluated on a variety of video sequences from different genres. Experimental results, in comparison with the most standard cut detection algorithms confirm our method is more robust to object and camera movements as well as illumination changes.     

U-curve: A branch-and-bound optimization algorithm for U-shaped cost functions on Boolean lattices applied to the feature selection problem

This paper presents the formulation of a combinatorial optimization problem with the following characteristics: (i) the search space is the power set of a finite set structured as a Boolean lattice; (ii) the cost function forms a U-shaped curve when applied to any lattice chain. This formulation applies for feature selection in the context of pattern recognition. The known approaches for this problem are branch-and-bound algorithms and heuristics that explore partially the search space. Branch-and-bound algorithms are equivalent to the full search, while heuristics are not. This paper presents a branch-and-bound algorithm that differs from the others known by exploring the lattice structure and the U-shaped chain curves of the search space. The main contribution of this paper is the architecture of this algorithm that is based on the representation and exploration of the search space by new lattice properties proven here. Several experiments, with well known public data, indicate the superiority of the proposed method to the sequential floating forward selection (SFFS), which is a popular heuristic that gives good results in very short computational time. In all experiments, the proposed method got better or equal results in similar or even smaller computational time.