The upgrade of topological group based on a new hyper-topology

Wang et al [1] have put forward the problem of upgrade of topology and obtained a series of systematic theories and applicable results. Li et al [2] have put forwarded the problem of upgrade of group and also obtained a series of results. Consequently, the problem of upgrade of mathematic structure...

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Bibliographic Details
Published inFuzzy information and engineering Vol. 3; no. 2; pp. 137 - 146
Main Authors Zhong, Yu-bin, Li, Hong-xing
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.06.2011
Taylor & Francis Group
Subjects
Computational Intelligence
Engineering
Fuzzy sets
Multiplication
Original Article
Topology
Fuzzy hyper-topological group
Fuzzy power set
Hyper-topological group
Power group
Upgrade
Power set
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Summary:Wang et al [1] have put forward the problem of upgrade of topology and obtained a series of systematic theories and applicable results. Li et al [2] have put forwarded the problem of upgrade of group and also obtained a series of results. Consequently, the problem of upgrade of mathematic structure has drawn more attention of researchers. However, for the work to upgrade topology and group at the same time, little progress has been made although there are someone studying on it. Based on a kind of intuitive convergent way, the paper has proposed a new hyper-topology and upgraded two mathematic structures of topological group to power set and fuzzy power set respectively. It has proved that multiplication and contradiction operations continues in the new hyper-topology after upgrading and a series of results are obtained creating hyper-topological group and fuzzy hyper-topological group. Accordingly, hyper-topological group and fuzzy hyper-topological group can be created, obtaining a breakthrough to upgrade topological group to its power set and fuzzy power set.
ISSN:1616-8658
1616-8666
DOI:10.1007/s12543-011-0072-y