关于t-模的旋转不变性

On the Rotation Invariance of t-norms

本文讨论t-模的旋转不变性。首先,我们给出了旋转不变t-模的基本性质,然后集中研究了该条件与彭等提出的条件(Ι)之间的关系。我们得到的主要结果是:若(T,S,n)是一个De Morgan三元组,则T关于n满足旋转不变性的充分必要条件是n为强非、(T,n)满足矛盾律且(T,S)满足条件(Ι)。

In this paper, we deal with the rotation invariance of t-norms. First, we give some basic properties of rotation invariant t-norms. Then, we concentrate on the investigation into the relationships between the rotation invariance and Condition （I） proposed by Peng etc. The main result we obtain is that if （T,S,n） is a De Morgan triple, then a necessary and sufficient condition for the rotation invariance is that n is a strong negation, （T,n） satisfies the law of contradiction and （T.S） satisfies Condition （I）.