On fuzzifying matroids: Dual matroids and spanning

Sun, Shoubin; Xiu, Zhen-Yu; Li, Lingqiang

doi:10.3233/ifs-141428

Cited by 5 publications

(1 citation statement)

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“…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%