Abstract:Several extensions and generalizations of fuzzy sets have been introduced in the literature, for example, Atanassov's intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets. In this paper, we propose hesitant fuzzy sets. Although from a formal point of view, they can be seen as fuzzy multisets, we will show that their interpretation differs from the two existing approaches for fuzzy multisets. Because of this, together with their definition, we also introduce some basic operations. In addition, we also study their relationship with intuitionistic fuzzy sets. We prove that the envelope of the hesitant fuzzy sets is an intuitionistic fuzzy set. We prove also that the operations we propose are consistent with the ones of intuitionistic fuzzy sets when applied to the envelope of the hesitant fuzzy sets. © 2010 Wiley Periodicals, Inc.
摘要:文献中已经介绍了模糊集的几个扩展和推广,例如,Atanassov的直觉模糊集、类型2模糊集和模糊多集。在这篇文章中,我们提出了犹豫模糊集。虽然从形式的角度来看,它们可以被视为模糊多集,但我们将证明它们的解释不同于现有的两种模糊多集的方法。正因为如此,结合它们的定义,我们还介绍了一些基本的运算。此外,我们还研究了它们与直觉模糊集的关系。证明了犹豫模糊集的包络是直觉模糊集。我们还证明了当应用于犹豫模糊集的包络时,我们提出的运算与直觉模糊集的运算是一致的。©2010 Wiley期刊,Inc.
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