One special subalgebra of the algebra of fuzzy truth values is the set of those elements that take only 0 and 1 as values. This subalgebra is in one-to-one correspondence with the subsets of the unit interval, but the operations do not correspond to ordinary union and intersection. The automorphisms of this subalgebra are studied here, resulting in showing that the subobjects corresponding to nite subsets is a characteristic subalgebra of the algebra of fuzzy truth values, and that the subalgebra corresponding to closed intervals is also a characteristic subalgebra. A number of facts about the automorphisms of the subalgebra in question are proved, but we have not yet succeeded in showing that it is a characteristic subalgebra of the algebra of fuzzy truth values
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