Measuring the directional distance between fuzzy sets
Measuring the directional distance between fuzzy sets
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DOI：
10.2139/ssrn.2828347
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发表时间：
2013-01
期刊：
影响因子：
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通讯作者：
Josie McCulloch;Christian Wagner;U. Aickelin
中科院分区：
文献类型：
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作者：
Josie McCulloch;Christian Wagner;U. Aickelin
模糊集之间的距离度量是模糊集理论中的一个基本工具。然而，目前文献中的距离度量并没有考虑模糊集之间变化的方向；在各种应用程序中都是一个有用的概念，比如用词计算。在本文中，我们强调了这种效用，并引入了一种考虑集合之间方向的距离度量。详细介绍了它在正态和非正态模糊集以及凸和非凸模糊集上的应用。我们使用来自MovieLens数据集的真实数据演示了新的距离度量，并建立了测量模糊集之间方向的好处。
The measure of distance between two fuzzy sets is a fundamental tool within fuzzy set theory. However, current distance measures within the literature do not account for the direction of change between fuzzy sets; a useful concept in a variety of applications, such as Computing With Words. In this paper, we highlight this utility and introduce a distance measure which takes the direction between sets into account. We provide details of its application for normal and non-normal, as well as convex and non-convex fuzzy sets. We demonstrate the new distance measure using real data from the MovieLens dataset and establish the benefits of measuring the direction between fuzzy sets.