论文标题
$ Q $ -VFCA：$ Q $ - 州矢量值模糊蜂窝自动机
$q$-VFCA: $q$-state Vector-valued Fuzzy Cellular Automata
论文作者
论文摘要
基本模糊细胞自动机（CA）被称为基本Ca的连续对应物，它是2态CA，通过局部规则的多项式表示。在本文中，我们首先开发了一种新的模糊方法，以$ q $ - 州的ca。它基于$ q $ - 州CA的向量表示，也就是说，$ q $ state被分配给$ q $维真实空间的标准基础向量，并且本地规则可以由$ q $ polynomials的元组表示。然后，$ q $ - 州矢量值模糊CA是通过将各州的集合扩展到标准基础矢量的凸形船体的定义的。状态的向量表示使我们能够以系统的方式列举3态矢量价值模糊CA的数字规则。
Elementary fuzzy Cellular Automata (CA) are known as continuous counterpart of elementary CA, which are 2-state CA, via the polynomial representation of local rules. In this paper, we first develop a new fuzzification methodology for $q$-state CA. It is based on the vector representation of $q$-state CA, that is, the $q$-states are assigned to the standard basis vectors of the $q$-dimensional real space and the local rule can be expressed by a tuple of $q$ polynomials. Then, the $q$-state vector-valued fuzzy CA are defined by expanding the set of the states to the convex hull of the standard basis vectors in the $q$-dimensional real space. The vector representation of states enables us to enumerate the number-conserving rules of 3-state vector-valued fuzzy CA in a systematic way.
