Since it was firstly introduced by Torra and Narukawa (The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, 2009, pp. 1378–1382), the hesitant fuzzy set has attracted more and more attention due to its powerfulness and efficiency in representing uncertainty and vagueness. This paper extends the classical VIKOR (vlsekriterijumska optimizacija i kompromisno resenje in serb...

Neutrosophic hesitant fuzzy set is the generalization of neutrosophic set and the hesitant fuzzy set, which can easily express the uncertain, incomplete and inconsistent information in cognitive activity, and the VIKOR (from Serbian:VIseKriterijumska Optimizacija I Kompromisno Resenje) method is an effective decision making tool which can select the optimal alternative by the maximum ‘‘group ut...

Hesitant fuzzy set is a very useful technique in the situations where there are some difficulties in determining the membership of an element to a set. Some aggregation methods have been developed for hesitant fuzzy information. Current aggregation methods are under the assumption that the criteria are at the same priority level. However, in real decision making problems, criteria have differen...

In recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type n fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual hesitant fuzzy sets DHFSs , which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy...

Hesitant fuzzy sets are very useful to deal with group decision making problems when experts have a hesitation among several possible memberships for an element to a set. During the evaluating process in practice, however, these possible memberships may be not only crisp values in [0,1], but also interval values. In this study, we extend hesitant fuzzy sets by intuitionistic fuzzy sets and refe...

The dual hesitant fuzzy linguistic term set (DHFLTS) is defined by two functions that express the grade of membership and non-membership using a terms. In present work, we first quote an example to point out existing complement operation DHFLTS on wrong track. Meanwhile, redefine this fill holes in ones. Next, notion information energy under background provided order build criteria weight deter...

Single-valued neutrosophic hesitant fuzzy set (SVNHFS) is a combination of single-valued neutrosophic set and hesitant fuzzy set, and its aggregation tools play an important role in the multiple criteria decision-making (MCDM) process. This paper investigates the MCDM problems in which the criteria under SVNHF environment are in different priority levels. First, the generalized single-valued ne...

Motivated by the idea of single valued neutrosophic uncertain linguistic sets (SVNULSs) and hesitant fuzzy sets (HFSs), in this article we combine SVNULSs with HFSs to present the idea of hesitant single valued neutrosophic uncertain linguistic sets (HSVNULSs), hesitant single valued neutrosophic uncertain linguistic elements (HSVNULEs) and defined some basic operational laws of HSVNULEs. We al...