Abstract

Fuzzy subalgebras are defined to be mappings from an algebra to a poset (which can be a lattice, and also the interval [0,1]), so that every level subset is an ordinary subalgebra. Every fuzzy subalgebra has a canonical representation, a mapping from the algebra to the poset of levels. Necessary and sufficient conditions under which a fuzzy subalgebra can be explicitly described by a suitable formula in lattice theoretic terms are given. Classes of algebras for which the poset of fuzzy subalgebras is a lattice are characterized.

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