Hesitant fuzzy sets
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.
Cite this
Vicenç Torra (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems. https://doi.org/10.1002/int.20418
@article{vicen2010hesitant,
title = {Hesitant fuzzy sets},
author = {Torra, Vicenç},
year = {2010},
journal = {International Journal of Intelligent Systems},
doi = {10.1002/int.20418}
}Citations in this library
Stored only when both papers are in the corpus — 3,161 citations exist upstream.