Some properties of relation information systems under homomorphisms

Wang, Changzhong; Wu, Congxin; Chen, Degang; Du, Wenju

doi:10.1016/j.aml.2007.10.006

Cited by 37 publications

(26 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence, P ∈ red(R). Note that Theorem 4.7(1) is not the corollary of Theorem 4.4 in [20]. Then, we have the following remark.…”

Section: Theorem 47 Let (U R) ∼ F (Vr) If (U R) Be a Knowledge Bmentioning

confidence: 88%

See 1 more Smart Citation

Relationships between knowledge bases and related results

Liu

et al. 2015

Knowl Inf Syst

View full text Add to dashboard Cite

Relationships between information systems are very important topics in the field of artificial intelligence. The concept of homomorphisms is an effective mathematical tool to study relationships between information systems. A knowledge base is a special relation information system. This paper investigates invariant characteristics of knowledge bases under the homomorphism. The fact that knowledge bases themselves are invariant and inverse invariant under the homomorphism is firstly proved. Next, some invariant characteristics and inverse invariant characteristics under the homomorphism, such as the dependency of knowledge bases, knowledge reductions, coordinate families and necessary relations, are obtained based on this fact. Finally, lattice characteristics of the dependency of knowledge bases are given. These results will be significant for establishing a framework of granular computing in knowledge bases.

show abstract

“…Hence, P ∈ red(R). Note that Theorem 4.7(1) is not the corollary of Theorem 4.4 in [20]. Then, we have the following remark.…”

Section: Theorem 47 Let (U R) ∼ F (Vr) If (U R) Be a Knowledge Bmentioning

confidence: 88%

“…Li et al [7] has earlier studied invariant characteristics of information systems under some homomorphism. Wang et al [16][17][18]20,21] have widely researched generalized information systems under homomorphisms. Zhu et al [26,27] have also done some work in this aspect.…”

Section: Introductionmentioning

confidence: 99%

Relationships between knowledge bases and related results

Liu

et al. 2015

Knowl Inf Syst

View full text Add to dashboard Cite

show abstract

“…Therefore, the study of communication between two ordered information systems is essentially to investigate the relationship between two classes of dominance relations. In this section, we first review the extension principle of classical sets to relations defined in [4,8].…”

Section: Invariant Properties Of Dominance Relations Under Relation Mmentioning

confidence: 99%

“…This requires studying the relationship between two information systems. Although in recent years many topics on information systems have been widely investigated [5][6][7][8][9][10][11][12][13][14][15][16][17][18], there are only a few researches focusing on communication between information systems [4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Some invariant properties of ordered information systems under homomorphism

Wang

Chen

2010

Sci. China Inf. Sci.

Self Cite

View full text Add to dashboard Cite

In this paper, some properties of ordered information systems under homomorphism are investigated. The concept of a consistent function with respect to dominance relations is first introduced and its properties are investigated. Then, some main invariant properties of dominance relations under relation mappings are studied. It is proven that attribute reductions in the original ordered information system and its image system are equivalent under the condition of homomorphism. By means of the results, we can get the smaller image system that has the same reducts as a given massive ordered information system.

show abstract

“…Note that the notion of homomorphism was introduced in [35] to study the relation between two information systems in order to obtain a smaller information system where their description functions are identical. Later, other invariants of information systems with respect to different classes of homomorphism were considered by several scholars for different cases, such as [36][37][38][39]32,[40][41][42], to mention a few. Up to the knowledge of the authors, there are no studies on homomorphism and its relation to reduction of data volume, except [22] which discussed the problem of data volume reduction in the sense of removing unnecessary elements of a covering.…”

Section: Introductionmentioning

confidence: 99%

Data volume reduction in covering approximation spaces with respect to twenty-two types of covering based rough sets

Shakiba

Hooshmandasl

2016

International Journal of Approximate Reasoning

View full text Add to dashboard Cite

In this paper, we investigate whether consistent mappings can be used as homomorphism mappings between a covering based approximation space and its image with respect to twenty-two pairs of covering upper and lower approximation operators. We also consider the problem of constructing such mappings and minimizing them. In addition, we investigate the problem of reducing the data volume using consistent mappings as well as the maximum amount of their compressibility. We also apply our algorithms against several datasets.

show abstract

Some properties of relation information systems under homomorphisms

Cited by 37 publications

References 6 publications

Relationships between knowledge bases and related results

Relationships between knowledge bases and related results

Some invariant properties of ordered information systems under homomorphism

Data volume reduction in covering approximation spaces with respect to twenty-two types of covering based rough sets

Contact Info

Product

Resources

About