Abstract: Type-2 fuzzy sets can deal directly with high uncertainties and have very strong practical application background. In this paper, a new type-2 fuzzy similarity measure is proposed on the basis of the axiom definitions of type-2 fuzzy similarity measures. Furthermore, it combines similarity measures with Yang and Shih’s algorithm as a clustering method for type-2 fuzzy data, and compares clustering results with Yang and Lin’s method. Examples show that the proposed measure is more reasonable. It also discusses attribute reduction of type-2 fuzzy information system based on type-2 fuzzy similarity measures, and the discernibility function method on appropriate reduction is given. Specific calculation steps of the reduction approach are presented by an example.

Key words: type-2 fuzzy sets, similarity, clustering analysis, type-2 fuzzy information system, attribute reduction

摘要： 二型模糊集可以直接处理高度不确定性，并且具有很强的实际应用背景。基于二型模糊相似度的公理化定义，给出了新的二型模糊相似度计算公式。进一步，将二型模糊相似度与Yang-Shih方法相结合，用于二型模糊数据的聚类分析，聚类结果与Yang-Lin的结果进行了比较，实例表明新的相似度更合理。此外，基于二型模糊相似度，讨论了二型模糊信息系统的属性约简问题，给出了相应约简的分辨函数法，并通过实例说明了该方法的具体计算步骤。

关键词: 二型模糊集, 相似度, 聚类分析, 二型模糊信息系统, 属性约简