Relationships between generalized rough sets based on covering and reflexive neighborhood system

Zhang, Yan-Lan; Li, Changqing; Lin, Menglei; Lin, Yaojin

doi:10.1016/j.ins.2015.05.023

Cited by 39 publications

(18 citation statements)

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“…Therefore apr NS is a closure operator. 5 Characterization of covering S for apr S being a closure operator Zhang, Li and Lin defined a special covering S and investigated twenty-three types of covering-based rough sets proposed in [49] which can be treated as the generalized rough sets based on neighborhood systems. In this section, we will discuss the properties of apr S and give the Characterization of covering S for apr S being a closure operator.…”

Section: Some Propositions Of Ns(u)mentioning

confidence: 99%

“…2 (Subsystem based definition [49]). Suppose S D .S ; S/ is a pair of subsystems of P.U /, S is a closure system and S is the dual system of S .…”

Section: Definition 51 ([49])mentioning

confidence: 99%

“…T.Lin et al defined some approximation operators which are based on neighborhood systems and did some research on them [52]. In addition, Y. Zhang et al discussed the relationships between generalized rough sets based on covering and reflexive neighborhood system [49] and proposed the operator apr S . Based on their works, we will investigate the properties of NS.U / and S. We also give characterizations for apr NS , apr S being closure operators.…”

Section: Introductionmentioning

confidence: 99%

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The characterizations of upper approximation operators based on special coverings

Wang

2017

Open Mathematics

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Abstract:In this paper, we discuss the approximation operators apr NS and apr S which are based on NS.U / and S. We not only obtain some properties of NS.U / and S, but also give examples to show some special properties. We also study sufficient and necessary conditions when they become closure operators. In addition, we give general and topological characterizations of the covering for two types of covering-based upper approximation operators being closure operators.

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Section: Some Propositions Of Ns(u)mentioning

confidence: 99%

“…2 (Subsystem based definition [49]). Suppose S D .S ; S/ is a pair of subsystems of P.U /, S is a closure system and S is the dual system of S .…”

Section: Definition 51 ([49])mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The characterizations of upper approximation operators based on special coverings

Wang

2017

Open Mathematics

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“…Lin [45,46] and Yao [47] discussed the approximation retrieval and information retrieval based on general neighborhood systems, respectively. 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

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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.

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“…Employing an IF implicator I and an IF t -norm T on L * , Zhou et al [68] defined the upper and lower approximations of IFSs w.r.t. an IF approximation space as follows: Definition 2.15.…”

Section: Introductionmentioning

confidence: 99%