In this paper, we define a new fuzzy squareness measure to quantify how much a given fuzzy shape matches a fuzzy square. The new fuzzy shape-based measure is naturally defined and theoretically well-founded, resulted in that its behavior can be understood and predicted in advance. It runs through the interval $(0,1]$ and takes the maximum value equals 1 if and only if the shape measured is a fuzzy square. The new fuzzy squareness measure is also invariant to similarity transformations. Several various experiments to illustrate the behavior of the new measure, and to verify all the theoretically proven results are also shown. Effectiveness and usefulness of the new fuzzy squareness measure are demonstrated in the tasks of object classification performed on three large well-known modern image datasets such as MPEG-7 CE-1, Swedish Leaf, and Portuguese Leaves datasets.

在本文中，我们定义了一种新的模糊平方度度量，以量化给定模糊形状与模糊平方相匹配的程度。新的基于模糊形状的度量是自然定义的，并且在理论上是有根据的，因此可以提前了解和预测其行为。它贯穿整个间隔$（0，\mathrm{1个}]$并且仅当所测量的形状是模糊正方形时才取最大值等于1。新的模糊平方度度量也不变于相似性变换。还显示了一些不同的实验，以说明新措施的行为，并验证所有理论上证实的结果。在对三个大型的现代著名图像数据集（如MPEG-7 CE-1，Swedish Leaf和Portuguese Leafs数据集）执行的对象分类任务中，证明了新模糊直方性度量的有效性和实用性。