模糊粗糙集的相似度量和相似性方向

粗糙集理论是一种新的处理模糊和不确定性知识的软计算工具,在人工智能及认知科学等众多领域已经得到了广泛的应用。相似度量的研究是模糊集理论与粗糙集理论的热点问题之一。文章提出了一种更精确、更合理的相似度量方法,讨论了它的一些性质。然后,在此基础上提出了模糊粗糙集的相似性方向的概念,用于比较两个相似的模糊粗糙集所包含信息的精确性大小,并给出了一个关于相似性方向的判别函数。这在近似推理、模式识别和决策分析等领域有着广泛的应用。最后,通过一个实例,分析说明了这种相似度量方法和相似性方向的判别方法是更合理更有效的。

Similarity Measure and Similarity Direction between Fuzzy Rough Sets

Rough set theory is emerging as a powerful tool for dealing with vagueness and uncertainty of facts,which has important applications to artificial intelligence and cognitive science.The research on similarity measure is important to both fuzzy set theory and rough set theory.In this paper,a new approach of similarity measure on fuzzy rough sets is presented,which is more reasonable and more effective.Then the concept of similarity direction between two fuzzy rough sets is proposed to describe which one could give more accurate information.Finally,by an example,it is verified that this similarity measure is more reasonable and more effective in practice.