2型模糊集的交并及与(1,2)-双切的连接

EUSFLAT Conf. Pub Date : 2011-08-06 DOI:10.2991/eusflat.2011.135

Z. Takác̆

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引用次数: 3

摘要

已知1型模糊集的标准相交与并集(即最小t范数与最大t保形下的相交与并集)是1型模糊集的唯一可切运算。本文的目的是证明对于一类2模糊集，对于某些特殊的切割，也具有类似的性质。如前所述，在α-平面上，2型模糊集的交集和并集不保持。因此，我们研究了另一种切割，即所谓的双重切割，并证明了在这种双重切割中，2型模糊集的相交和并保持不变。

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Intersection and union of type-2 fuzzy sets and connection to (1, 2)-double cuts

It is known that the standard intersection and union of type-1 fuzzy sets (i.e., the intersection and union under the minimum t-norm and maximum tconorm) are the only cutworthy operations for type1 fuzzy sets. The aim of this paper is to show that similar property holds also for type-2 fuzzy sets, with respect to some special cutting. As was already demonstrated, the intersection and union of type-2 fuzzy sets are not preserved in α-planes. Thus, we study another kind of cutting, so-called double cuts, and show that the intersection and union of type-2 fuzzy sets are preserved in these double cuts.

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EUSFLAT Conf.

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