On the transitivity of a parametric family of cardinality-based similarity measures
On the transitivity of a parametric family of cardinality-based similarity measures
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DOI：
10.1016/j.ijar.2008.03.006
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
B. Baets;S. Janssens;H. Meyer
中科院分区：
文献类型：
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作者：
B. Baets;S. Janssens;H. Meyer
我们为有限宇宙上的普通集合引入了一个基于基数的相似度量的参数族，其中包含许多众所周知的相似度量。我们刻划了这一族的Ł-ukasiewicz传递成员和乘积传递成员。它们的重要性源于它们与伪度量的一一对应。然后使用基于可交换准Copula的模糊化方案将普通集合的相似性度量转换为模糊集合的相似性度量，使其适用于对象的分级特征集表示。本文的主要结果是在模糊化过程中保持了及物性，因此也保留了相应的双重度量解释。
We introduce a parametric family of cardinality-based similarity measures for ordinary sets (on a finite universe) harbouring numerous well-known similarity measures. We characterize the Łukasiewicz-transitive and product-transitive members of this family. Their importance derives from their one-to-one correspondence with pseudo-metrics. Fuzzification schemes based on a commutative quasi-copula are then used to transform these similarity measures for ordinary sets into similarity measures for fuzzy sets, rendering them applicable on graded feature set representations of objects. The main result of this paper is that transitivity, and hence also the corresponding dual metric interpretation, is preserved along this fuzzification process.