A vector similarity measure for linguistic approximation: Interval type-2 and type-1 fuzzy sets
A vector similarity measure for linguistic approximation: Interval type-2 and type-1 fuzzy sets
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DOI：
10.1016/j.ins.2007.04.014
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发表时间：
2008-01
期刊：
影响因子：
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通讯作者：
Dongrui Wu;J. Mendel
中科院分区：
文献类型：
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作者：
Dongrui Wu;J. Mendel
模糊逻辑经常用于文字计算（CWW）。当CWW引擎的输入词由区间2型模糊集（IT2 FS）建模时，CWW引擎的输出也可以是IT2 FS，A FS，它需要映射到语言标签，以便可以理解。因为每个语言标签由IT2 FS B i表示，所以需要比较A i和B i的相似性以找到与A i最相似的B i。本文提出了一种适用于IT2流媒体系统的向量相似性度量（VSM），它的两个元素分别度量了流媒体系统在形状和邻近度上的相似性。一个比较研究表明，VSM给出了更合理的结果比所有其他现有的相似性措施IT2 FS的语言近似问题。此外，VSM还可以用于类型1 FS，这是所有不确定性消失时IT2 FS的特殊情况。
Fuzzy logic is frequently used in computing with words (CWW). When input words to a CWW engine are modeled by interval type-2 fuzzy sets (IT2 FSs), the CWW engine’s output can also be an IT2 FS, A∼, which needs to be mapped to a linguistic label so that it can be understood. Because each linguistic label is represented by an IT2 FS B∼i, there is a need to compare the similarity of A∼ and B∼ito find the B∼imost similar to A∼. In this paper, a vector similarity measure (VSM) is proposed for IT2 FSs, whose two elements measure the similarity in shape and proximity, respectively. A comparative study shows that the VSM gives more reasonable results than all other existing similarity measures for IT2 FSs for the linguistic approximation problem. Additionally, the VSM can also be used for type-1 FSs, which are special cases of IT2 FSs when all uncertainty disappears.