Linear fuzzifying uniformities

The main purpose of this paper is to study Hutton type fuzzifying uniformities on linear spaces. Firstly, we show that if a base of a fuzzifying uniformity defined over a linear space is translation-invariant, balanced and absorbed, then it generates a linear fuzzifying topology. From this linear fu...

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Published inJournal of intelligent & fuzzy systems Vol. 40; no. 6; pp. 10453 - 10464
Main Authors Jin, Zhen-Yu, Yan, Cong-Hua
Format Journal Article
LanguageEnglish
Published London, England SAGE Publications 01.01.2021
Sage Publications Ltd
Subjects
Topology
Vector spaces
fuzzy norm
Linear fuzzifying uniformity
linear fuzzifying topology
complete boundedness
Hausdorff separation axiom
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Summary:The main purpose of this paper is to study Hutton type fuzzifying uniformities on linear spaces. Firstly, we show that if a base of a fuzzifying uniformity defined over a linear space is translation-invariant, balanced and absorbed, then it generates a linear fuzzifying topology. From this linear fuzzifying topology, we can construct a new linear fuzzifying uniformity (i.e., a fuzzifying uniformity compatible with the linear structure) which is equivalent to the original fuzzifying uniformity. Secondly, the Hausdorff separation and complete boundedness in linear fuzzifying uniformities are investigated. In addition, as an example, the linear fuzzifying uniformity induced by a fuzzy norm is also discussed.
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ISSN:1064-1246
1875-8967
DOI:10.3233/JIFS-200702