Reconstructing Concept Lattices Using nth-Order Context Kernels

To be different from traditional algorithms for concept lattice constructing, a method based on nth-order context kernel is suggested in this paper. The context kernels support generating small lattices for sub-contexts split by a given context. The final concept lattice is reconstructed by combining these small lattices. All relevant algorithms are implemented in a system IsoFCA. Test shows that the method yields concept lattices in lower time complexity than Godin algorithm in practical case.

Concept Lattice Construction through the Composition and Decomposition of Formal Contexts

The purpose of this paper is to study the construction of concept lattice from variable formal contexts.Composition and decomposition theories are proposed for the unraveling of concept lattice from contexts with variable attribute set in the process of information updating.The relationship between the extension sets of the original context and that of its sub-context is analyzed.The composition and decomposition theories are then generalized to the situation involving more than two sub-contexts and the situation with variable attribute set and object set.

Attribute reduction theory and approach to concept lattice

The theory of the concept lattice 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. This paper proposes the theory of attribute reduction in the concept lattice, which extends the theory of the concept lattice. In this paper, the judgment theorems of consistent sets are examined, and the discernibility matrix of a formal context is introduced, by which we present an approach to attribute reduction in the concept lattice. The characteristics of three types of attributes are analyzed.

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.

Research on Two Main Construction Methods of Concept Lattices

Because of the completeness of concept lattices, the time complexity of constructing concept lattices has become the main factor affecting the application of formal concept analysis(FCA). The key problems in the research of concept lattices are how to improve the generation efficiency and how to reduce the space and time complexity of constructing concept lattices. So far, reviews on lattice construction algorithms have not been comprehensive. In view of this situation, we give a detailed review on two categories of construction algorithms:batch methods and incremental methods. The first category is a formal context that cannot be updated once the concept lattice has been constructed; the second category is a formal context that can be updated after a new object being added to the formal context. We briefly introduce classical and improved construction methods, illustrate the deficiencies of some algorithms and point out the improvements of the follow-up algorithms. Furthermore, we compare and discuss several key algorithms, and also pay attention to the application of concept lattices. Finally,two further research directions of concept lattices are proposed, including parallel construction methods of concept lattices and research of heterogeneous data concept lattices.

Basic theorem as representation of heterogeneous concept lattices

We propose a method for representing heteroge- neous concept lattices as classical concept lattices. Particu- larly, we describe a transformation of heterogeneous formal context into a binary one, such that corresponding concept lattices will be isomorphic. We prove the correctness of this transformation by the basic theorem for heterogeneous as well as classical concept lattices.

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.

Permission and role automatic assigning of user in role-based access control

Role mining and setup affect the usage of role-based access control(RBAC).Traditionally,user's role and permission assigning are manipulated by security administrator of system.However,the cost is expensive and the operating process is complex.A new role analyzing method was proposed by generating mappings and using them to provide recommendation for systems.The relation among sets of permissions,roles and users was explored by generating mappings,and the relation between sets of users and attributes was analyzed by means of the concept lattice model,generating a critical mapping between the attribute and permission sets,and making the meaning of the role natural and operational.Thus,a role is determined by permission set and user's attributes.The generated mappings were used to automatically assign permissions and roles to new users.Experimental results show that the proposed algorithm is effective and efficient.

Subposition Assembly-Based Construction of Non-Frequent Concept Semi-Lattice

An efficient way to improve the efficiency of the applications based on formal concept analysis （FCA） is to construct the needed part of concept lattice used by applications. Inspired by this idea, an approach that constructs lower concept semi-lattice called non-frequent concept semi-lattice in this paper is introduced, and the method is based on subposition assembly. Primarily, we illustrate the theoretical framework of subposition assembly for non-frequent concept semi-lattice. Second, an algorithm called Nocose based on this framework is proposed. Experiments show both theoretical correctness and practicability of the algorithm Nocose.

A scenario construction and similarity measurement method for navy combat search and rescue

Navy combat search and rescue(NCSAR) is an important component of the modern maritime warfare and the scenario of NCSAR is the basis for decision makers to rely on. According to the core elements in the NCSAR process, the NCSAR scenario structure is constructed from seven perspectives based on the multi-view architecture framework. According to the NCSAR scenarios evolution over time, the NCSAR scenario sequence is analyzed and modeled based on the concept lattice method. Then,the incremental construction algorithm of the NCSAR scenario sequence lattice is given. On this basis, the similarity measurement index of NCSAR scenarios is defined, and the similarity measurement model of NCSAR scenarios is proposed. Finally, the rationality of the method is verified by an example analysis. The NCSAR scenario and similarity measurement method proposed can provide scientific guidance for rapid making, dynamic adjustment and implementation of the NCSAR program, and thus improve the efficiency and effectiveness of NCSAR.

Fuzzy Set Approximations in Fuzzy Formal Contexts

In this paper, a kind of multi-level formal concept is introduced. Based on the proposed multi-level formal concept,we present a pair of rough fuzzy set approximations within fuzzy formal contexts.By the proposed rough fuzzy set approximations,we can approximate a fuzzy set according to different precision level.We discuss the properties of the proposed approximation operators in detail.

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.