论文标题
在三种类型的$ l $ -Fuzzy $β$基于覆盖的粗糙套装
On three types of $L$-fuzzy $β$-covering-based rough sets
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
In this paper, we mainly construct three types of $L$-fuzzy $β$-covering-based rough set models and study the axiom sets, matrix representations and interdependency of these three pairs of $L$-fuzzy $β$-covering-based rough approximation operators. Firstly, we propose three pairs of $L$-fuzzy $β$-covering-based rough approximation operators by introducing the concepts such as $β$-degree of intersection and $β$-subsethood degree, which are generalizations of degree of intersection and subsethood degree, respectively. And then, the axiom set for each of these $L$-fuzzy $β$-covering-based rough approximation operator is investigated. Thirdly, we give the matrix representations of three types of $L$-fuzzy $β$-covering-based rough approximation operators, which make it valid to calculate the $L$-fuzzy $β$-covering-based lower and upper rough approximation operators through operations on matrices. Finally, the interdependency of the three pairs of rough approximation operators based on $L$-fuzzy $β$-covering is studied by using the notion of reducible elements and independent elements. In other words, we present the necessary and sufficient conditions under which two $L$-fuzzy $β$-coverings can generate the same lower and upper rough approximation operations.
