Soft Computing

, Volume 21, Issue 7, pp 1803–1816

Hesitant fuzzy rough set over two universes and its application in decision making

Methodologies and Application

DOI: 10.1007/s00500-015-1882-3

Cite this article as:
Zhang, H., Shu, L. & Liao, S. Soft Comput (2017) 21: 1803. doi:10.1007/s00500-015-1882-3


In this paper, we propose a general decision-making framework based on the HF rough set model over two universes. By a constructive approach, the HF rough set model over two universes is first presented and some properties of this model are further discussed. The union, the intersection and the composition of hesitant fuzzy approximation spaces are proposed, and some properties are also investigated. We then give a new approach of decision making in uncertainty environment using the hesitant fuzzy rough sets over two universes. Finally, two practical applications are provided to illustrate the validity of this approach.


Hesitant fuzzy rough set Two universes Hesitant fuzzy approximation spaces Decision making 

Funding information

Funder NameGrant NumberFunding Note
the National Natural Science Foundation of China
  • 71261022

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China
  2. 2.School of Mathematics and Computer ScienceNorthwest University for NationalitiesLanzhouPeople’s Republic of China

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