Three-way Concept Research Articles

Variable-precision three-way concepts in L-contexts

The notion of fuzzy concept is proposed to deal with object-attribute data with L-values (where L is a truth-value structure). One disadvantage of fuzzy concept is that a fuzzy context contains a considerable number of fuzzy concepts. This makes it very time-consuming to generate a fuzzy concept lattice, and it is very difficult to find important concepts. In addition, the fuzzy concept shows great strictness when applying to crisp sets. To overcome these problems, we propose several new kinds of variable-precision concepts within L-contexts in this paper. First, we present two kinds of variable-precision two-way (VP2W) concepts: α-positive concept and β-negative concept. The family of each kind of VP2W concept forms a complete lattice. Next, considering both the positive and negative parts, we investigate two kinds of variable-precision three-way (VP3W) concepts: (α,β)-object-induced three-way concept and (α,β)-attribute-induced three-way concept. The family of each kind of VP3W concept forms a complete lattice. Then, we study the relationships between VP2W concepts and VP3W concepts. The results show that VP3W concept lattices can be directly generated by VP2W concept lattices. Finally, the experiments are preformed to verify the effectiveness of our model.

Dynamic Three-Way Concept Learning Model Based on PS-Rough Set

The PS-rough set adds the dynamic characteristics of the elements moving in and moving out of the set, and introduces it into the three-way concept learning, and establishes the dynamic three-way concept learning model based on the PS-rough set. Firstly, the related definitions of dynamic three-way concept learning are introduced, and the calculation method of conditional probability function is given. Secondly, the related dynamic characteristics of the dynamic three-way concept learning model are proposed and proved, and the dynamic three-way concept learning algorithm is given, and the validity of the algorithm are verified by an example. Finally, the dynamic three-way concept learning model solves the dynamic change problem of the sample subset, reduces the computation of the probability of the condition, and gives a simple three-way concept division method.

Attribute reduction of SE-ISI concept lattices for incomplete contexts.

Three-way concept analysis in incomplete contexts lays the theory dealing with the data in incomplete contexts, especially three kinds of partially known formal concepts including SE-ISI formal concept, ISE-SI formal concept and ISE-ISI formal concept. Generally speaking, not every attribute is essential in an incomplete context since the purpose of research is different. Thus, we propose four kinds of attribute reduction of SE-ISI concept lattices based on different criteria. Then, we discuss the relationships among the four kinds of attribute reduction, including the relationships among the consistent sets and relationships among the reducts. Finally, based on discernibility matrices and discernibility functions, the approaches to obtaining these attribute reduction are presented.

Double threshold construction method for attribute‐induced three‐way concept lattice in incomplete fuzzy formal context

Concept lattice theory is the basis of formal concept analysis. It is an effective tool for knowledge representation and discovery. Three-way decision theory is a new decision theory based on rough sets and decision rough sets. In this study, a method is proposed for constructing attribute-induced three-way concept lattices in an incomplete fuzzy formal context. First, the authors introduce the related knowledge of the classical formal context, the fuzzy formal context and incomplete fuzzy formal context in detail. They put forward a method to fill the incomplete formal context. Secondly, they propose a double threshold operation, which divides the relationship between objects and attributes into three parts: belonging, not belonging and undetermined. Thirdly, they propose three methods to complement incomplete formal context and introduce their advantages and disadvantages. Fourthly, they deal with incomplete formal context by special symbol completion method and get related algorithms of attribute-induced three-way concept lattice. Finally, a case is given to verify the effectiveness of the algorithm for constructing attribute-induced three-way concept lattices.

On relationship between three-way concept lattices

By reformulating and extending the properties of three-way operators, this paper investigates the relationship between different kinds of three-way concept lattices. Three-way operators are defined through eight kinds of two-way operators which are connected by the complement operation. To examine the interrelations systematically, we study (a) the relationship between two-way operators, (b) the relationship between two-way concepts, (c) the relationship between three-way operators, and (d) the relationship between three-way concepts. The results show that the four kinds of object-induced three-way concept lattices are order isomorphic to each other and the four kinds of attribute-induced three-way concept lattices are also order isomorphic to each other.

Constructing three-way concept lattice based on the composite of classical lattices

Three-way concept analysis provides a novel model for three-way decisions, and also extends the classical formal concept analysis, which has attracted many attentions in recent years. In order to construct three-way concept lattices, original formal context and its complement context need to be considered simultaneously. In this paper, a new method of constructing attribute-induced three-way (AE) and object-induced three-way (OE) concept lattices is proposed. Firstly, we introduce an AE-oriented composite operator and an OE-oriented composite operator that combine a pair of formal concepts coming from the concept lattices of original formal context and its complement context. Secondly, we define the candidate AE concepts and redundant AE concepts based on the AE-oriented composite operator, and define the candidate OE concepts and redundant OE concepts based on the OE-oriented composite operator, respectively. Finally, we propose an AE lattice construction algorithm and an OE lattice construction algorithm. Theoretical analysis and experimental results demonstrate that the proposed method is simple and effective, and it is a useful supplement to current three-way concept lattice construction methods.

The dynamic update method of attribute-induced three-way granular concept in formal contexts

Granular computing is becoming a very hot research field, which has received extensive attention in recent years. It helps us to analyze and solve problems better by dividing complex problems into several simpler ones. Three-way granular concept is an important concept proposed by combining granular computing, formal concept analysis and three-way decision. Using traditional updating methods of three-way granular concepts, a lot of time and space resources are needed when multiple attributes or objects are deleted in formal context. In order to improve the efficiency and flexibility of obtaining three-way concepts, this paper discusses a novel dynamic update method of three-way granular concepts. In this paper, we firstly introduce the related knowledge of three-way granular concepts. Secondly, the update rules of the extension and connotation of attribute-induced three-way granular concepts are discussed in the dynamic formal context to construct three-way granular concepts. Moreover, we develop a method for establishing attribute-induced three-way granular concept by dynamic changes in the case of deleting multiple objects and attributes in the formal context. Furthermore, we design four algorithms to compare between the proposed approaches and traditional updating ways of three-way granular concepts. Finally, the validity of dynamic update method of attribute-induced three-way granular concept is verified through the experimental evaluation using six datasets coming from the University of California-Irvine (UCI) repository.

Three-way rough semiconcept

Three-way decisions, as a better way than two-way decisions, has played an important role in many fields. As an extension of formal concept, rough semiconcept constitutes a new approach for data analysis. By now, three-way concept, which combines three-way decisions with formal concept, has been an efficient tool for knowledge representation problems. Hence, we want to further apply three-way decisions to rough semiconcept. In this work, we introduce three-way rough semiconcept by an example, which combines rough semiconcept with the assistant of three-way decisions. After that, we attain the structure of all three-way rough semiconcepts from an algebraic perspective. Furthermore, we give two kinds of approximation operators, which can characterize three-way rough semiconcepts. Finally, we present algorithms for searching three-way rough semiconcepts. An example is to demonstrate the correct and effective of algorithms in this paper.

Intuitionistic fuzzy three-way formal concept analysis based attribute correlation degree

As an important expanded of the classical formal concept, the three-way formal concept analysis integrates more information with the three-way decision theory. However, to the best of our knowledge, few scholars have studied the intuitionistic fuzzy three-way formal concept analysis. This paper proposes an intuitionistic fuzzy three-way formal concept analysis model based on the attribute correlation degree. To achieve this, we comprehensively analyze the composition of attribute correlation degree in the intuitionistic fuzzy environment, and introduce the corresponding calculation methods for different situations, as well as prove the related properties. Furthermore, we investigate the intuitionistic fuzzy three-way concept lattice ((IF3WCL) of object-induced and attribute-induced. Then, the relationship between the IF3WCL and the positive, negative and boundary domains in the three-way decision are discussed. In addition, considering the final decision problem of boundary objects, the secondary decision strategy of boundary objects is obtained for IF3WCL. Finally, a numerical example of multinational company investment illustrates the effectiveness of the proposed model. In this paper, we systematically study the IF3WCL, and give a quantitative analysis method of formal concept decision along with its connection with three-way decision, which provides new ideas for the related research.

Conflict analysis under one-vote veto based on approximate three-way concept lattice

Conflict analysis, which plays an important role in our society, has attracted more and more attentions. However, the existing conflict analysis models are not effective enough to evaluate the inconsistency degree of cliques that have more than two individuals. Besides, for each clique, its allied, conflict and neutral attributes have not been explicitly defined and thoroughly explored. Therefore, due to the lack of enough explicit clues, we cannot further formulate some strategies manipulating the conflict degrees of related cliques to realize the specific objectives. Last but not least, one-vote veto is seldom considered, although it plays a vital role in many fields, such as venture capital and United Nations Security Council resolutions. In order to solve these problems, we resort to three-way concept analysis and describe a clique by using the intent of a specific concept. On the basis of the obtained specific concepts, we derive the allied, conflict and neutral attributes of cliques, and further make decisions and explore the maximal coalitions and minimum conflict sets. Finally, in order to cater dynamic environment, we also describe an incremental algorithm for conflict analysis.

Rules acquisition of formal decision contexts based on three-way concept lattices

Three-way concept lattices can supply much more information than classical concept lattices since they contain the positive information and negative information between objects and attributes simultaneously. Taking advantage of this, the rules acquisition for formal decision contexts from the perspective of three-way concept lattices are discussed, and the results are compared with the common decision rules based on classical concept lattices. Firstly, the definition of object-induced three-way consistence of a formal decision context is presented. Then, positive decision rules and negative decision rules are proposed for an object-induced three-way consistent formal decision context. Furthermore, we give semantic explanation for these rules, and compare them with common rules obtained from a strongly consistent lattice. In parallel, the similar issues are investigated from the perspective of attributes, including the definition of attribute-induced three-way consistence of a formal decision context, rules acquisition based on an attribute-induced three-way consistent formal decision context, and rules comparison. Finally, the relationships among the three types of consistence, namely, object-induced three-way consistence, attribute-induced three-way consistence, and existing strongly consistence are discussed to make the contents compact. Some theoretical examples are given to illustrate the main results of this paper.

Influences of Three-Way Concept Lattice Caused by Variations of Attribute Values

Three-way concept lattices have been widely used in various types of applications. As the construction of three-way concept lattices is rather time consuming, especially for large formal contexts, it is not applicable to construct the lattices from the beginning when changes are made to the contexts. Motivated by this problem, the influences of three-way concept lattices caused by variations of attribute values are explored in this study. Specifically, we discuss two types of changes. One is changing the value of a specific incidence relation from 0 to 1, and the other is from 1 to 0. Furthermore, two types of three-way concept lattices are investigated. One is the object-induced three-way concept lattice, and the other is the attribute-induced three-way concept lattice. Both the mathematical proofs and the examples show the effectiveness of our proposed methods.

Three-way dual concept analysis

Three-way concept analysis is a mathematical theory, which combines formal concept analysis and three-way decision. The existing models, i.e., three-way concept lattices and three-way object oriented concept lattices, have been used successfully in many fields. However, these two models are established to cater some specific applications and cannot fulfill some special requirements such as the needs to seek potential collaborators in international import and export transactions. In this paper, a novel type of three-way concept lattices is presented based on dual concept analysis, which enables ones to characterize specific set by pointing out the attributes that are not possessed by at least one object in the complement of this specific set. And then, the connections between three-way dual concept lattices and classical dual concept lattices are explored. Besides, the relationships among four types of three-way concept analysis models, i.e., three-way concept lattices, three-way dual concept lattices, three-way object oriented concept lattices and three-way property oriented concept lattices, are investigated.

Unlabelled text mining methods based on two extension models of concept lattices

Concept lattice is a useful tool for text extraction. The common text clustering method fails to generate hierarchical relationships among categories and realize soft clustering simultaneously, while the concept lattice ignores the negative correlation between an object subset and an attribute subset. Motivated by the problems, we propose unlabelled text mining methods based on fuzzy concept lattice and three-way concept lattice. Firstly, we excavate hierarchical text categories to construct a classification system based on fuzzy concept lattice, and the labelled samples are obtained by the word matching method. Then, we construct a three-way concept lattice to get positive and negative classification rules based on the labelled samples, and the classifier is constructed to predict the new samples. Finally, Sogou laboratory news corpus is used to evaluate the efficiency of text clustering and classification methods. The results demonstrate that the improved clustering method has a higher average cluster goodness than earlier procedures and the classification model based on three-way concept lattice achieves a higher accuracy.

A theoretical study on the object (property) oriented concept lattices based on three-way decisions

The three-way object oriented lattice and the three-way property oriented lattice are extend researches of rough concept analysis by combining three-way decisions. In this paper, we investigate them more comprehensively and detailedly. Firstly, the relationship between the object (property) oriented concept lattice and the three-way object (property) oriented concept lattice is studied, respectively. In addition, approaches to construct two types of three-way concept lattices based on apposition and subposition of formal contexts are given based on these relationships. Finally, since the methods for constructing three-way concept lattices and three-way object oriented and property oriented concept lattices are similar, the connections among them are discussed.

Granule description based knowledge discovery from incomplete formal contexts via necessary attribute analysis

Incomplete formal contexts are an extension of the classical formal contexts in which the relationship between some objects and attributes is unknown according to the current information. In fact, incomplete formal contexts are frequently encountered in human cognitive activities. This paper discusses knowledge discovery from incomplete formal contexts based on necessary attribute analysis, including granule description, cognitive concept learning and approximate decision rule mining. Specifically, we put forward a novel granule description method for knowledge discovery so that three-way concepts can be formed by attribute enrichment, and approximate decision rules can be mined via the detailed and concise descriptions of granules. Compared to the existing work, the time complexity of mining approximate decision rules is reduced sharply since only the closely related granules are needed in the proposed granule description method.

A Novel Interval Three-Way Concept Lattice Model with Its Application in Medical Diagnosis

Medical diagnosis has been recognized as one of the key processes in clinical medicine, which determines diseases from some given symptoms. Nonetheless, previous works about medical diagnosis have some drawbacks because medical data are usually fuzzy, uncertain, incomplete and imprecise. To achieve the optimal medical diagnosis decision by reducing cost and enhancing accuracy, this paper develops a new method named interval three-way concept lattice model. Firstly, we redefine the decision rules and metric function of three-way decision based on interval concept lattice. Secondly, we build a visualized hierarchical structure of relationship between concepts through interval concept construction algorithm which helps us to make decision preferably and clearly. Finally, we establish a dynamic strategy optimization model for medical diagnosis decision making. In addition, a medical case demonstrates the effectiveness and feasibility of this proposed model.

Three-Way Concept Analysis for Incomplete Formal Contexts

Recently, incomplete formal contexts have received more and more attention from the communities of formal concept analysis. Different from a complete context where the binary relations between all the objects and attribute are known, an incomplete formal context has at least a pair of object and attribute with a completely unknown binary relation. Partially known formal concepts use interval sets to indicate the incompleteness. Three-way formal concept analysis is capable of characterizing a target set by combining positive and negative attributes. However, how to describe target set, by pointing out what attributes it has with certainty and what attributes it has with possibility and what attributes it does not has with certainty and what attributes it does not has with possibility, is still an open problem. This paper combines the ideas of three-way formal concept analysis and partially known formal concepts and presents a framework of approximate three-way concept analysis. At first, approximate object-induced and attribute-induced three-way concept lattices are introduced, respectively. And then, the relationship between approximate three-way concept lattice and classical three-way concept lattice are investigated. Finally, examples are presented to demonstrate and verify the obtained results.

L-fuzzy concept analysis for three-way decisions: basic definitions and fuzzy inference mechanisms

In this paper, the basic ideas underlying fuzzy logic are introduced into the study of three-way formal concept analysis. This leads naturally to the notion of L-fuzzy three-way concepts. The L-fuzzy three-way operators and their inverse are defined and their properties are given. Based on these operators, two types of L-fuzzy three-way concepts are defined and the corresponding three-way concept lattices are constructed. A possibility theory reading of L-fuzzy three-way concepts is also provided. Moreover, the corresponding fuzzy inference method is studied. Two coherent fuzzy inference methods, the lower approximate fuzzy inference and the upper approximate fuzzy inference, are proposed, respectively.

Relationships between three-way concepts and classical concepts

Relationships between three-way concepts and classical concepts