Axiomatization on generalized neighborhood system-based rough sets

Zhao, Fangfang; Li, Lingqiang

doi:10.1007/s00500-017-2957-0

Cited by 27 publications

(12 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Next, we recall the notions of L-fuzzy generalized neighborhood systems and rough approximation operators based L-fuzzy generalized neighborhood systems. Definition 1 (see [49,50]). Let X be a set; the function N: X ⟶ L L X is called an L-fuzzy generalized neighborhood system operator on X, if for any x ∈ X, ∨ C∈L X N(x)(C) � 1.…”

Section: (B C) and S(c A) ≤ S(c B) (S3) S(a B) * S(c D) ≤ S(a * C B * D) (S4) S(a B) * S(b C) ≤ S(a C) (S5) S(a ∧ T∈t A T ) � ∧ T∈t S(a Amentioning

confidence: 99%

“…Definition 2 (see [49,50]). Let N: X ⟶ L L X be an L-fuzzy generalized neighborhood system operator.…”

Section: (B C) and S(c A) ≤ S(c B) (S3) S(a B) * S(c D) ≤ S(a * C B * D) (S4) S(a B) * S(b C) ≤ S(a C) (S5) S(a ∧ T∈t A T ) � ∧ T∈t S(a Amentioning

confidence: 99%

“…Recently, the notion of generalized neighborhood systems is proposed and used to define a theory of rough set, called generalized neighborhood system-based rough sets [45,[47][48][49]. In [49,50], Zhao and Li gave an axiomatic characterization on generalized neighborhood system-based rough sets. Hence, it is natural to establish fuzzy general rough sets by fuzzifying them, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, it is natural to establish fuzzy general rough sets by fuzzifying them, respectively. Quite recently, by fuzzifying the notion of generalized neighborhood systems, Zhao and Li [49,50] established a rough set model based on L-fuzzy generalized neighborhood systems. It was proved that this model brought the fuzzy relation-based rough set model, fuzzy covering-based rough set model, and generalized neighborhood system-based rough set models under a unified framework.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Lattice Structures of Approximation Operators Based on L-Fuzzy Generalized Neighborhood Systems

et al. 2021

View full text Add to dashboard Cite

Following the idea of L -fuzzy generalized neighborhood systems as introduced by Zhao et al., we will give the join-complete lattice structures of lower and upper approximation operators based on L -fuzzy generalized neighborhood systems. In particular, as special approximation operators based on L -fuzzy generalized neighborhood systems, we will give the complete lattice structures of lower and upper approximation operators based on L -fuzzy relations. Furthermore, if L satisfies the double negative law, then there exists an order isomorphic mapping between upper and lower approximation operators based on L -fuzzy generalized neighborhood systems; when L -fuzzy generalized neighborhood system is serial, reflexive, and transitive, there still exists an order isomorphic mapping between upper and lower approximation operators, respectively, and both lower and upper approximation operators based on L -fuzzy relations are complete lattice isomorphism.

show abstract

Section: (B C) and S(c A) ≤ S(c B) (S3) S(a B) * S(c D) ≤ S(a * C B * D) (S4) S(a B) * S(b C) ≤ S(a C) (S5) S(a ∧ T∈t A T ) � ∧ T∈t S(a Amentioning

confidence: 99%

“…Definition 2 (see [49,50]). Let N: X ⟶ L L X be an L-fuzzy generalized neighborhood system operator.…”

Section: (B C) and S(c A) ≤ S(c B) (S3) S(a B) * S(c D) ≤ S(a * C B * D) (S4) S(a B) * S(b C) ≤ S(a C) (S5) S(a ∧ T∈t A T ) � ∧ T∈t S(a Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Lattice Structures of Approximation Operators Based on L-Fuzzy Generalized Neighborhood Systems

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Wang [48], Syau [49], and Zhang [50] investigated relationships between reflexive generalized neighborhood system-based rough sets and other rough sets. Quite recently, the second author and his coauthor [51] discussed the axiomatic characterization on approximation operators based on generalized neighborhood systems.…”

Section: Introductionmentioning

confidence: 99%

A New Approach to Rough Set Based on Remote Neighborhood Systems

Sun

2019

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

The notion of neighborhood systems is abstracted from the geometric notion of “near”, and it is primitive in the theory of topological spaces. Now, neighborhood systems have been applied in the study of rough set by many researches. The notion of remote neighborhood systems is initial in the theory of topological molecular lattice, and it is abstracted from the geometric notion of “remote”. Therefore, the notion of remote neighborhood systems can be considered as the dual notion of neighborhood systems. In this paper, we develop a theory of rough set based on remote neighborhood systems. Precisely, we construct a pair of lower and upper approximation operators and discuss their basic properties. Furthermore, we use a set of axioms to describe the lower and upper approximation operators constructed from remote neighborhood systems.

show abstract

A rough set model based on fuzzifying neighborhood systems

Jin

Bing-xue

et al. 2020

Soft Comput

View full text Add to dashboard Cite

Axiomatization on generalized neighborhood system-based rough sets

Cited by 27 publications

References 37 publications

The Lattice Structures of Approximation Operators Based on L-Fuzzy Generalized Neighborhood Systems

The Lattice Structures of Approximation Operators Based on L-Fuzzy Generalized Neighborhood Systems

A New Approach to Rough Set Based on Remote Neighborhood Systems

A rough set model based on fuzzifying neighborhood systems

Contact Info

Product

Resources

About