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.

中文翻译：

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类型2模糊集真值代数的子代数

摘要 本文首先在二类模糊集真值代数的约简中引入一些子代数，并证明其中一个是二分格。然后我们也得到了二类模糊集真值代数的子代数形成二分格的三个充要条件。接下来我们研究这种双半格的一些子代数及其表征。最后，我们介绍了一些不同于二分格的子代数，并展示了一个函数是凸函数的充分必要条件。