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\(L\)-fuzzy subfields and \(L\)-fuzzy linear spaces. (Chinese. English summary) Zbl 1046.15003

Summary: We introduce the concepts of \(L\)-fuzzy subfields and \(L\)-fuzzy linear spaces over \(L\)-fuzzy subfields, where \(L\) is a completely distributive lattice. Furthermore, we give some characterizations by the theory of \(L_\alpha\)-nested sets and \(L_\beta\)-nested sets.

MSC:

15A03 Vector spaces, linear dependence, rank, lineability
06D10 Complete distributivity
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
08A72 Fuzzy algebraic structures
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