Pedrycz W, Vukovich G
Dept. of Electr. & Comput. Eng., Alberta Univ., Edmonton, Alta.
IEEE Trans Syst Man Cybern B Cybern. 2000;30(2):249-62. doi: 10.1109/3477.836374.
The study introduces a concept of relevance of fuzzy mappings regarded as fundamental constructs of granular computing and rule-based systems, in particular. The notion of relevance of the fuzzy mappings is instrumental in the quantification of the quality of such mappings prior to their detailed construction. For the purposes of such quantification, we introduce shadowed sets and discuss as an algorithmic framework to be instrumental in expressing and quantifying the property of relevance of the fuzzy mappings. It is revealed that shadowed sets provide an interesting three-valued quantification of this property (such as acceptable mapping, marginal mapping, and a lack of mapping). The paper includes a number of detailed calculations concerning two commonly exploited classes of triangular and Gaussian fuzzy sets. Numerical studies are discussed as well.
该研究引入了模糊映射相关性的概念，特别是将其视为粒度计算和基于规则系统的基本构造。模糊映射的相关性概念有助于在详细构建此类映射之前对其质量进行量化。为了进行这种量化，我们引入了阴影集，并将其作为一个算法框架进行讨论，该框架有助于表达和量化模糊映射的相关性属性。结果表明，阴影集为该属性提供了一种有趣的三值量化（例如可接受映射、边际映射和缺乏映射）。本文包括了一些关于两类常用的三角模糊集和高斯模糊集的详细计算。还讨论了数值研究。
