Dual hesitant fuzzy information aggregation with Einstein t-conorm and t-norm

  • Hua Zhao
  • Zeshui Xu
  • Shousheng Liu


Dual hesitant fuzzy set (DHFS) is a new generalization of fuzzy set (FS) consisting of two parts (i.e., the membership hesitancy function and the non-membership hesitancy function), which confronts several different possible values indicating the epistemic degrees whether certainty or uncertainty. It encompasses fuzzy set (FS), intuitionistic fuzzy set (IFS), and hesitant fuzzy set (HFS) so that it can handle uncertain information more flexibly in the process of decision making. In this paper, we propose some new operations on dual hesitant fuzzy sets based on Einstein t-conorm and t-norm, study their properties and relationships and then give some dual hesitant fuzzy aggregation operators, which can be considered as the generalizations of some existing ones under fuzzy, intuitionistic fuzzy and hesitant fuzzy environments. Finally, a decision making algorithm under dual hesitant fuzzy environment is given based on the proposed aggregation operators and a numerical example is used to demonstrate the effectiveness of the method.


Dual hesitant fuzzy set Einstein t-conorm and t-norm operation aggregation operator 


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Copyright information

© Systems Engineering Society of China and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.College of SciencesPLA University of Science and TechnologyNanjing, JiangsuChina
  2. 2.Business SchoolSichuan UniversityChengdu, SichuanChina

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