Extended hesitant fuzzy sets (EHFSs), which allow the membership degree of an element to a set represented by several possible value-groups, can be considered as a powerful tool to express uncertain information in the process of group decision making. Therefore, we derive some correlation coefficients between EHFSs, which contain two cases, the correlation coefficients taking into account the l...

Background: In this paper, a generic hesitant fuzzy set (HFS) model for clustering various ECG beats according to weights of attributes is proposed. A comprehensive review of the electrocardiogram signal classification and segmentation methodologies indicates that algorithms which are able to effectively handle the nonstationary and uncertainty of the signals should be used for ECG analysis. Ex...

Since the seminal paper of fuzzy set theory by Zadeh in 1965, many extensions have been proposed to overcome the difficulty for assigning the membership degrees. In recent years, a new extension, the hesitant fuzzy sets, has attracted a lot of interest due to its usefulness to handle those problems in which it is difficult to provide accurately a single membership value; since for hesitant sets...

Since its original formulation, the theory of fuzzy sets has spawned a number of extensions where the role of membership values in the real unit interval $[0, 1]$ is handed over to more complex mathematical entities. Amongst the many existing extensions, two similar ones, the fuzzy multisets and the hesitant fuzzy sets, rely on collections of several distinct values to represent fuzzy membershi...

Assuming a linguistic framework, a model for the consensus reaching problem in heterogeneous group decision making is proposed. This model contains two types of linguistic consensus measures: linguistic consensus degrees and linguistic proximities to guide the consensus reaching process. These measures evaluate the current consensus state in three levels of action: level of the pairs of alterna...

In this paper a Sequential Selection Process in Group Decision Making under linguistic assessments is presented, where a set of linguistic preference relations represents individuals preferences. A collective linguistic preference is obtained by means of a deened linguistic ordered weighted averaging operator whose weights are chosen according to the concept of fuzzy majority, speciied by a fuz...

Fuzzy set theory provides a framework in which natural language expressions can be modelled mathematically, thereby even taking the vagueness of linguistic terms into account. In fuzzy systems a linguistic term (e.g. fast) is represented by a fuzzy set, while a linguistic modifier (e.g. very) is modelled by an operator (also known as hedge) transforming a fuzzy set into another. In the paper fi...

With respect to multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant fuzzy elements, the traditional grey relational projection (GRP) method is extended to solve multiple attribute decision making problems under hesitant fuzzy environment. Based on the hesitant fuzzy decision matrix provided by decision makers, all feasible alternatives are ...

Fuzzy decision making is the collection of single or multicriteria techniques aiming at selecting the best alternative in case of imprecise, incomplete, and vague data. This chapter reviews the fuzzy decision making literature and summarizes the review results by tabular and graphical illustrations. The classification is based on the new extensions of fuzzy sets: Intuitionistic, hesitant, and t...

Hesitant fuzzy linguistic preference relation (HFLPR) is of interest because it provides an efficient way for opinion expression under uncertainty. For enhancing the theory group decision making (GDM) with HFLPR, paper introduces a method addressing GDM based on consistency and consensus measurements, which involves (1) defining hesitant geometric index (HFLGCI) proposing algorithm checking inc...