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Lattice of fuzzy subalgebras and closure systems in \(I^ X\). (English) Zbl 0731.08007

For a given universal algebra \(A=[X,F]\) with a specified set F of finitary operations on the set X, each operation is extended to a finitary operation on the lattice \(I^ X\) of fuzzy subsets of X over the unit interval of real numbers \(I=[0,1]\). It is shown that the lattice of fuzzy subalgebras of A is an algebraic closure system in \(I^ X\) according to an appropriate definition.

MSC:

08A99 Algebraic structures
06B99 Lattices
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References:

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