The axiomatic characterizations on <i>L</i>-generalized fuzzy neighborhood system-based approximation operators

Zhao, Fangfang; Jin, Qiu; Li, Lingqiang

doi:10.1080/03081079.2017.1407928

Cited by 29 publications

(9 citation statements)

References 58 publications

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“…In the future work, we shall establish a reduction theory of remote neighborhood-based rough sets. Quite recently, the second author and his coauthor also fuzzify the notion of generalized neighborhood systems and then develop a theory of fuzzy rough sets based on fuzzy general neighborhood systems [59]. In [60], the author and his coauthor discussed the dual matroids and spanning; we shall also consider a theory of fuzzy rough sets and fuzzy matroids based on fuzzy general remote systems, which played an important role in the theory of fuzzy topological spaces.…”

Section: Discussionmentioning

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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Section: Discussionmentioning

confidence: 99%

A New Approach to Rough Set Based on Remote Neighborhood Systems

Sun

2019

Mathematical Problems in Engineering

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“…Let µ, ν be L-fuzzy sets in X. The subsethood degree [37][38][39][40] of µ, ν, denoted by S X (µ, ν), is defined by…”

Section: Preliminariesmentioning

confidence: 99%

p-Topologicalness—A Relative Topologicalness in ⊤-Convergence Spaces

Li¹

2019

Mathematics

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In this paper, p-topologicalness (a relative topologicalness) in ⊤-convergence spaces are studied through two equivalent approaches. One approach generalizes the Fischer’s diagonal condition, the other approach extends the Gähler’s neighborhood condition. Then the relationships between p-topologicalness in ⊤-convergence spaces and p-topologicalness in stratified L-generalized convergence spaces are established. Furthermore, the lower and upper p-topological modifications in ⊤-convergence spaces are also defined and discussed. In particular, it is proved that the lower (resp., upper) p-topological modification behaves reasonably well relative to final (resp., initial) structures.

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“…Let µ, ν be L-fuzzy sets in X. The subsethood degree of µ, ν, denoted as S X (µ, ν), is defined by [44][45][46] Lemma 1. [31,42,47] Let f : X −→ Y be a function and…”

Section: Preliminariesmentioning

confidence: 99%

p-Regularity and p-Regular Modification in ⊤-Convergence Spaces

Jin

Lang

2019

Mathematics

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Fuzzy convergence spaces are extensions of convergence spaces. ⊤-convergence spaces are important fuzzy convergence spaces. In this paper, p-regularity (a relative regularity) in ⊤-convergence spaces is discussed by two equivalent approaches. In addition, lower and upper p-regular modifications in ⊤-convergence spaces are further investigated and studied. Particularly, it is shown that lower (resp., upper) p-regular modification and final (resp., initial) structures have good compatibility.

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The axiomatic characterizations on L-generalized fuzzy neighborhood system-based approximation operators

Cited by 29 publications

References 58 publications

A New Approach to Rough Set Based on Remote Neighborhood Systems

A New Approach to Rough Set Based on Remote Neighborhood Systems

p-Topologicalness—A Relative Topologicalness in ⊤-Convergence Spaces

p-Regularity and p-Regular Modification in ⊤-Convergence Spaces

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