Abstract
In this paper, we first introduce some subalgebras in a reduct of the truth value algebra of type-2 fuzzy sets and prove one of them is a bisemilattice. Then we also obtain three necessary and sufficient conditions under which subalgebras of the truth value algebra of type-2 fuzzy sets form a bisemilattice. Next we investigate some subalgebras of this kind of bisemilattice and their characterizations. Finally, we introduce some subalgebras different from the bisemilattice and show a necessary and sufficient condition that a function is convex.
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