论文标题
多级粒状近似通过分离和相邻模糊颗粒
Multi-class granular approximation by means of disjoint and adjacent fuzzy granules
论文作者
论文摘要
在颗粒计算中，模糊集可以通过可与原始模糊集W.R.T.尽可能接近的粒状代表集近似。给定的紧密度量。这样的集合称为粒状近似。在本文中，我们介绍了脱节和相邻颗粒的概念，并研究了新定义如何影响颗粒状近似值。首先，我们表明，新概念对于二进制分类问题很重要，因为它们有助于使决策区域分开（分离颗粒），同时涵盖了属性空间（相邻颗粒）。后来，我们考虑了多类分类问题的颗粒状近似，导致多级颗粒近似的定义。最后，我们展示了如何有效地计算出多级粒状近似值的olukasiewicz模糊连接。我们还提供图形插图，以更好地理解引入的概念。
In granular computing, fuzzy sets can be approximated by granularly representable sets that are as close as possible to the original fuzzy set w.r.t. a given closeness measure. Such sets are called granular approximations. In this article, we introduce the concepts of disjoint and adjacent granules and we examine how the new definitions affect the granular approximations. First, we show that the new concepts are important for binary classification problems since they help to keep decision regions separated (disjoint granules) and at the same time to cover as much as possible of the attribute space (adjacent granules). Later, we consider granular approximations for multi-class classification problems leading to the definition of a multi-class granular approximation. Finally, we show how to efficiently calculate multi-class granular approximations for Łukasiewicz fuzzy connectives. We also provide graphical illustrations for a better understanding of the introduced concepts.
