Hesitant Fuzzy Set and Its Extensions

  • Bahram FarhadiniaEmail author
  • Zeshui Xu
Part of the Uncertainty and Operations Research book series (UOR)


In this chapter, we first introduce briefly the concepts of classical sets and fuzzy sets (FSs). Then, we deal with the main concepts of this book, that is, hesitant fuzzy sets (HFSs). Through this part of the book, we provide the readers with the related topics of HFSs, including, fundamental definitions, basic operations, different kinds of negations, S-norms and T-norms together with two kinds of ordering methods for HFSs. Then, as the first generalization of HFS, the interval-valued HFSs (IVHFSs) are defined, and the main algebraic operations are presented. The next part of the chapter is devoted to introducing another extension of HFS, called dual HFS (DHFS). As needed later, the DHFS-based algebraic operations are reviewed in this section. The other generalized type of HFS, named higher order HFS (HOHFS), is reviewed. Finally, the concept of hesitant fuzzy linguistic term set (HFLTS) is introduced, and the chapter ends with the two rules of comparison of HFLTSs.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Quchan University of TechnologyQuchanIran
  2. 2.Business SchoolSichuan UniversityChengduChina

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