Cognitive Computation

, Volume 9, Issue 1, pp 81–94 | Cite as

Distance and Aggregation-Based Methodologies for Hesitant Fuzzy Decision Making

  • B. FarhadiniaEmail author
  • Zeshui Xu


Hesitant fuzzy set (HFS) as an effective tool to reflect human’s hesitancy has received great attention in recent years. The importance weights of possible values in hesitant fuzzy elements (HFEs), which are the basic units of a HFS, have not been taken into account in the existing literature. Thus, the frequently used HFEs cannot deal with the situations where all the possible values are provided by experts with different levels of expertise. Consequently, in this paper, we propose an extension of typical HFS called the ordered weighted hesitant fuzzy set (OWHFS). The basic units of an OWHFS allow the membership of a given element to be defined in terms of several possible values together with their importance weights. Moreover, in order to indicate that the OWHFS has a good performance in decision making, we first present some information measures and several aggregation operators for OWHFSs. Then, we apply them to multi-attribute decision making with ordered weighted hesitant fuzzy information.


Ordered weighted hesitant fuzzy set (OWHFS) Distance measure Similarity measure Aggregation operator Multi-attribute decision making 



The work was partly supported by the National Natural Science Foundation of China (Nos. 61273209, 71571123).

Compliance with Ethical Standards

Conflict of interests

Authors declare that they have no conflict of interest. This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsQuchan University of Advanced TechnologyQuchanIran
  2. 2.Business SchoolSichuan UniversityChengduPeople’s Republic of China

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