A new concept of equivalence between intervals and the induced indistinguishability between interval‐valued (IV) fuzzy sets are proposed and considered. A new notion of the degree of IV equivalence is presented where partial or linear orders and the width of intervals are involved reflecting uncertainty. Furthermore, construction methods of the considered equivalences are provided and the relation between them and other notions of IV equivalences are studied. Finally, a methodology to apply the proposed equivalences in the field of image processing is shown, along with an illustrative example.

中文翻译：

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考虑图像处理不确定性的区间值对等度量

提出并考虑了区间之间的等价性和区间值（IV）模糊集之间的诱导的不可区分性的新概念。提出了IV等价度的新概念，其中涉及部分或线性阶数以及区间的宽度，反映了不确定性。此外，提供了考虑的等价物的构造方法，并研究了它们与IV等价物的其他概念之间的关系。最后，连同说明性示例一起，示出了一种在图像处理领域中应用所提出的等价物的方法。