## 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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