Multiple set is a newborn member of the family of generalized sets, which can model uncertainty together with multiplicity. It has the power to handle numerous uncertain features of objects in a multiple way. Multiple set theory has the edge over the well established fuzzy set theory by its capability to handle uncertainty and multiplicity simultaneously. Similarity measure of fuzzy sets is well addressed in literature and has found prominent applications in various domains. As multiple set is an efficient generalization of fuzzy set, the concept and theory of similarity measure can be extended to multiple set theory and can be developed probable applications in various real-life problems. This paper introduces the concept of similarity measure of multiple sets and proposes two different similarity measures of multiple sets and investigates their properties. Finally, this work substantiates application of the concept of similarity measure of multiple sets to pattern recognition. A numerical illustration demonstrates the effectiveness of the proposed technique to this application.

中文翻译：

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多组相似度测度及其在模式识别中的应用

多重集是广义集家族的新生成员，它可以将不确定性与多重性一起建模。它有能力以多种方式处理对象的众多不确定特征。多集理论由于其同时处理不确定性和多重性的能力而优于成熟的模糊集理论。模糊集的相似性度量在文献中得到了很好的解决，并且在各个领域都有突出的应用。由于多集是模糊集的有效推广，相似性测度的概念和理论可以扩展到多集理论，并可以在各种实际问题中得到可能的应用。本文引入了多集相似性测度的概念，提出了两种不同的多集相似性测度，并研究了它们的性质。最后，这项工作证实了多组相似性度量概念在模式识别中的应用。数值插图证明了所提出的技术对该应用程序的有效性。