scholarly journals Rule Reductions of Decision Formal Context Based on Mixed Information

2021 ◽  
Author(s):  
Yidong Lin ◽  
Jinjin Li ◽  
Ju Huang
Keyword(s):  
Concept Lattice ◽  
Decision Rules ◽  
Negative Information ◽  
Formal Context ◽  
Classical Concept ◽  
Weak Basis ◽  
Concept Lattices ◽  
Rule Acquisition ◽  
Decision Formal Context

Abstract Three-way concept lattice extracts knowledge from positive and negative information separately. However, some applications require to mix positive and negative information for management and representation explicitly. In this paper, rule acquisition of FCA is extended based on mixed information. Firstly, two types of mixed concept lattices are studied. Then the relationships between mixed concept and classical concept, three-way concept are explored in depth. Secondly, mixed decision rules are investigated thoroughly. And the weak-basis is put forward to approximate to the basis of mixed decision rules. Finally, the comparison of mixed decision rules and three-way decision rules is perfectly discussed.

scholarly journals Attribute Extended Algorithm of Lattice-Valued Concept Lattice Based on Congener Formal Context

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Li Yang ◽  
Yang Xu
Keyword(s):  
Parallel Processing ◽  
Distributed Storage ◽  
Concept Lattice ◽  
Research Work ◽  
Sufficient Conditions ◽  
Formal Context ◽  
Concept Lattices ◽  
Lattice Implication Algebra ◽  
Implication Algebra ◽  
Necessary And Sufficient

This paper is the continuation of our research work about lattice-valued concept lattice based on lattice implication algebra. For a better application of lattice-valued concept lattice into data distributed storage and parallel processing, it is necessary to research attribute extended algorithm based on congener formal context. The definitions of attribute extended formal context and congener formal context are proposed. On condition that the extent set stays invariable when the new attribute is increased, the necessary and sufficient conditions of forming attribute values are researched. Based on these conditions, the algorithms of generating lattice-valued congener formal context and establishing concept lattice are given, by which we can provide a useful basis for union algorithm and constructing algorithm of lattice-valued concept lattices in distributed and parallel system.

The construction of multi-granularity concept lattices

2020 ◽  
Vol 39 (3) ◽  
pp. 2783-2790
Author(s):  
Qian Hu ◽  
Ke-Yun Qin
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Mutual Transformation ◽  
Concept Lattices ◽  
Construction Methods ◽  
Formal Concepts ◽  
Transformation Methods

The construction of concept lattices is an important research topic in formal concept analysis. Inspired by multi-granularity rough sets, multi-granularity formal concept analysis has become a new hot research issue. This paper mainly studies the construction methods of concept lattices in multi-granularity formal context. The relationships between concept forming operators under different granularity are discussed. The mutual transformation methods of formal concepts under different granularity are presented. In addition, the approaches of obtaining coarse-granularity concept lattice by fine-granularity concept lattice and fine-granularity concept lattice by coarse-granularity concept lattice are examined. The related algorithms for generating concept lattices are proposed. The practicability of the method is illustrated by an example.

scholarly journals A New Rapid Incremental Algorithm for Constructing Concept Lattices

Information ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 78 ◽  
Author(s):  
Jingpu Zhang ◽  
Ronghui Liu ◽  
Ligeng Zou ◽  
Licheng Zeng
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Incremental Algorithm ◽  
Formal Context ◽  
Formal Concept ◽  
Concept Lattices ◽  
Covering Relation ◽  
Canonical Generator ◽  
Lattice Construction ◽  
Time And Space Complexity

Formal concept analysis has proven to be a very effective method for data analysis and rule extraction, but how to build formal concept lattices is a difficult and hot topic. In this paper, an efficient and rapid incremental concept lattice construction algorithm is proposed. The algorithm, named FastAddExtent, is seen as a modification of AddIntent in which we improve two fundamental procedures, including fixing the covering relation and searching the canonical generator. The proposed algorithm can locate the desired concept quickly by adding data fields to every concept. The algorithm is depicted in detail, using a formal context to show how the new algorithm works and discussing time and space complexity issues. We also present an experimental evaluation of its performance and comparison with AddExtent. Experimental results show that the FastAddExtent algorithm can improve efficiency compared with the primitive AddExtent algorithm.

scholarly journals A Novel Incorporate Algorithm of Concept Lattice

2013 ◽  
Vol 756-759 ◽  
pp. 2803-2807
Author(s):  
Xi Gong
Keyword(s):  
Direct Product ◽  
Concept Lattice ◽  
Research Field ◽  
Formal Context ◽  
Concept Lattices ◽  
Product Operation ◽  
Single Attribute ◽  
Bottom To Top

With the expansion of the research field, the research object of some original seemingly unrelated properties have been studied together. At this time, the number of attribute in formal context has changed. For the increased attributes, we need to construct a new concept lattice. The existing incremental building algorithms of concept lattice need the original formal context as the basis, with single attribute or a set of attribute of the object to rebuild the concept lattice. They can't effectively utilize these existing concept lattice that have not relation in attributes. Here, the paper presents one new algorithm for incorporating concept lattice based on the existed concept lattices. We can directly build the together lattice from bottom to top by direct product operation on the existed concept lattices and the mapping relation between the direct product lattice of two existed concept lattices and the together lattice. Formal contexts that attribute sets have no intersection are fit for this algorithm.

Using Formal Concept Analysis and Rough Set Constructing the System of Semantic Web

2011 ◽  
Vol 58-60 ◽  
pp. 1664-1670
Author(s):  
Hong Sheng Xu ◽  
Rui Ling Zhang
Keyword(s):  
Semantic Web ◽  
Rough Set ◽  
Formal Concept Analysis ◽  
Rough Set Theory ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Great Promise ◽  
Formal Concept ◽  
Concept Lattices

Formal concept analysis (FCA) is based on a formalization of the philosophical understanding of a concept as a unit of thought constituted by its extent and intent. The rough set philosophy is founded on the assumption that with every object of the universe of discourse we associate some information. This paper deals with approaches to knowledge reduction in generalized consistent decision formal context. Finally, a new system model of semantic web based on FCA and rough set is proposed, which preserve more structural and featural information of concept lattice. In order to obtain the concept lattices with relatively less attributes and objects, we study the reduction of the concept lattices based on FCA and rough set theory. The experimental results indicate that this method has great promise.

Research on Web Dynamic Ontology Construction Based on Concept Lattice

2013 ◽  
Vol 411-414 ◽  
pp. 589-592
Author(s):  
Hua Zhu Song ◽  
Xiao Xue Wang ◽  
Lu Xu ◽  
Fan Zhou
Keyword(s):  
Information System ◽  
Concept Lattice ◽  
Formal Context ◽  
The Novel ◽  
Concept Lattices ◽  
Ontology Construction ◽  
Similarity Calculation ◽  
Novel Method ◽  
Stock Information ◽  
The Web

Ontology and semantic are very popular in Web, and the construction of Web dynamic ontology has been the problem urgent to be solved. Firstly, the basic framework for constructing Web dynamic ontology is shown. Next, the concept lattice is introduced, based on which the novel method of building Web dynamic ontology is given. It includes constructing the initial ontology, extracting web knowledge, generating the formal contexts, merging formal context, merging concept lattices with ontology-based similarity calculation, transforming the concept lattice to the ontology. At last, the stock information system is employed to verify the methods proposed. The results showed the stock ontology could be dynamically updated with the change from the Web, and we can get new inferred knowledge from the updated stock ontology by Racer; the method proposed is valid and feasible.

scholarly journals Rule Acquisition in Formal Decision Contexts Based on Formal, Object-Oriented and Property-Oriented Concept Lattices

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Yue Ren ◽  
Jinhai Li ◽  
Cherukuri Aswani Kumar ◽  
Wenqi Liu
Keyword(s):  
Numerical Experiments ◽  
Decision Rules ◽  
Object Oriented ◽  
Concept Lattices ◽  
Rule Acquisition

Rule acquisition is one of the main purposes in the analysis of formal decision contexts. Up to now, there have been several types of rules in formal decision contexts such as decision rules, decision implications, and granular rules, which can be viewed as∧-rules since all of them have the following form: “if conditions1,2,…,andmhold, then decisions hold.” In order to enrich the existing rule acquisition theory in formal decision contexts, this study puts forward two new types of rules which are called∨-rules and∨-∧mixed rules based on formal, object-oriented, and property-oriented concept lattices. Moreover, a comparison of∨-rules,∨-∧mixed rules, and∧-rules is made from the perspectives of inclusion and inference relationships. Finally, some real examples and numerical experiments are conducted to compare the proposed rule acquisition algorithms with the existing one in terms of the running efficiency.

scholarly journals The Method of Data Analysis in Intuitionistic Fuzzy Generalized Consistent Decision Formal Context

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 262
Author(s):  
Binbin Sang ◽  
Binghan Long ◽  
Jinzhong Pang ◽  
Weihua Xu
Keyword(s):  
Data Analysis ◽  
Lattice Theory ◽  
Fuzzy Theory ◽  
Concept Lattice ◽  
Attribute Reduction ◽  
Formal Context ◽  
Intuitionistic Fuzzy ◽  
Decision Formal Context ◽  
Intuitionistic Fuzzy Theory

Concept lattice has been successfully applied to various fields as an effective tool for data analysis and knowledge discovery, with attribute reduction being the key problem. This paper combines the intuitionistic fuzzy theory with the concept lattice theory and proposes one kind of concept lattice in intuitionistic fuzzy generalized consistent decision formal context. Furthermore, an approach to attribute a reduction in the discernibility matrix is proposed and investigated, making the discovery of implicit knowledge easier and the representation simpler in the data system and perfecting the theory of concept lattice. Moreover, this paper studies, in detail, the algorithms and case study of data analysis in the intuitionistic fuzzy generalized consistent decision formal context. The potential value of the method to deal with information discussed in this paper, especially the value of forecasting and decision-making, is expected in future.

Neutrosophic three-way concept lattice and its application in conflict analysis

2021 ◽  
pp. 1-18
Author(s):  
Han Yang ◽  
Keyun Qin
Keyword(s):  
Data Analysis ◽  
Knowledge Discovery ◽  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Conflict Analysis ◽  
Neutrosophic Set ◽  
Formal Context ◽  
Formal Concept ◽  
Concept Lattices

The theory of three-way concept analysis has been developed into an effective tool for data analysis and knowledge discovery. In this paper, we propose neutrosophic three-way concept lattice by combining neutrosophic set with three-way concept analysis and present an approach for conflict analysis by using neutrosophic three-way concept lattice. Firstly, we propose the notion of neutrosophic formal context, in which the relationships between objects and attributes are expressed by neutrosophic numbers. Three pairs of concept derivation operators are proposed. The basic properties of object-induced and attribute-induced neutrosophic three-way concept lattices are examined. Secondly, we divide the neutrosophic formal context into three classical formal contexts and propose the notions of the candidate neutrosophic three-way concepts and the redundant neutrosophic three-way concepts. Two approaches of constructing object-induced (attribute-induced) neutrosophic three-way concept lattices are presented by using candidate, redundant and original neutrosophic three-way concepts respectively. Finally, we apply the neutrosophic formal concept analysis to the conflict analysis and put forward the corresponding optimal strategy and the calculation method of the alliance.

scholarly journals The Feature Description of Formal Context Based on the Relationships among Concept Lattices

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1397
Author(s):  
Ting Qian ◽  
Yongwei Yang ◽  
Xiaoli He
Keyword(s):  
Concept Lattice ◽  
Object Oriented ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Type I ◽  
Type Ii ◽  
Concept Lattices ◽  
Feature Description ◽  
The Relationship

Three-way concept analysis (3WCA) is extended research of formal concept analysis (FCA) by combining three-way decision. The three-way object oriented concept lattice (OEOL) is one of the important data structures which integrates rough set, concept lattice and three-way decision in 3WCA. In the paper, we investigate the characteristics of formal context based on the isomorphic relationship among the kinds of concept lattices with OEOL. Firstly, II-dual intersectable attributes and II-dual intersectable context are proposed and the relationship between the type I-dual intersectable context(dual intersectable context) and the type II-dual intersectable context are studied. In addition, the relationship among the kinds of concept lattices with OEOL are studied when the formal context is both I-dual intersectable context and II-dual intersectable context. Finally, the inverse problems of the above conclusions are discussed and the following two conclusions are obtained: (1) the formal context is the type II-dual intersectable context, when the object oriented concept lattice and OEOL are isomorphic. (2) In addition, the formal context is the type I-dual intersectable context, when the concept lattice and OEOL are anti-isomorphic.

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