Hesitant Fuzzy Sets
Hesitant Fuzzy Sets
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DOI：
10.1002/int.20418
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发表时间：
2010-06-01
影响因子：
7
通讯作者：
Torra, Vicenc
中科院分区：
文献类型：
--
作者：
Torra, Vicenc
模糊集的几个扩展和推广已经在文献中介绍，例如，Atanassov的直觉模糊集，2型模糊集和模糊多集。在本文中，我们提出了犹豫模糊集。尽管从形式的角度来看，它们可以被视为模糊多重集，但我们将证明它们的解释与模糊多重集的两种现有方法不同。基于此，在给出它们的定义的同时，我们还介绍了一些基本的操作。此外，我们还研究了它们与直觉模糊集的关系。我们证明了犹豫模糊集的包络是一个直觉模糊集。我们还证明了我们提出的操作是一致的直觉模糊集的应用时，犹豫不决的模糊集的包络。(C)2010 Wiley Periodicals，Inc.
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. (C) 2010 Wiley Periodicals, Inc.