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Erschienen in:
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2014 | OriginalPaper | Buchkapitel

On the Intuitionistic Fuzzy Topological Structures of Rough Intuitionistic Fuzzy Sets

verfasst von : You-Hong Xu, Wei-Zhi Wu, Guoyin Wang

Erschienen in: Transactions on Rough Sets XVIII

Verlag: Springer Berlin Heidelberg

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Abstract

A rough intuitionistic fuzzy set is the result of approximation of an intuitionistic fuzzy set with respect to a crisp approximation space. In this paper, we investigate topological structures of rough intuitionistic fuzzy sets. We first show that a reflexive crisp rough approximation space can induce an intuitionistic fuzzy Alexandrov space. It is proved that the lower and upper rough intuitionistic fuzzy approximation operators are, respectively, an intuitionistic fuzzy interior operator and an intuitionistic fuzzy closure operator if and only if the binary relation in the crisp approximation space is reflexive and transitive. We then verify that a similarity crisp approximation space can produce an intuitionistic fuzzy clopen topological space. We further examine sufficient and necessary conditions that an intuitionistic fuzzy interior (closure, respectively) operator derived from an intuitionistic fuzzy topological space can associate with a reflexive and transitive crisp relation such that the induced lower (upper, respectively) rough intuitionistic fuzzy approximation operator is exactly the intuitionistic fuzzy interior (closure, respectively) operator.

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Metadaten
Titel
On the Intuitionistic Fuzzy Topological Structures of Rough Intuitionistic Fuzzy Sets
verfasst von
You-Hong Xu
Wei-Zhi Wu
Guoyin Wang
Copyright-Jahr
2014
Verlag
Springer Berlin Heidelberg
Buch
Transactions on Rough Sets XVIII

Print ISBN: 978-3-662-44679-9

Electronic ISBN: 978-3-662-44680-5

Copyright-Jahr: 2014

DOI
https://doi.org/10.1007/978-3-662-44680-5_1