The main aim of this paper is to present a novel method for ranking hesitant fuzzy sets (HFSs) based on transforming HFSs into fuzzy sets (FSs). The idea behind the method is an interesting HFS decomposition which is referred here to as the horizontal representation in the current study. To show the validity of the proposed ranking method, we apply it to solve a multi-attribute decision-making ...

In this paper, the study of the evolution of approximation space theory and its applications is considered in the context of rough sets introduced by Zdzis law Pawlak and information granulation as well as computing with words formulated by Lotfi Zadeh. Central to this evolution is the rough-mereological approach to approximation of information granules. This approach is built on the inclusion ...

Selecting the most suitable alternative under uncertainty is considered as a critical decision-making problem that affects the success of organizations. In the selection process, there are a number of assessment criteria, considered by a group of decision makers, which often could be established in a multi-level hierarchy structure. The aim of this paper is to introduce a new hierarchical multi...

Intuitionistic fuzzy probabilities are an extension of the concept of probabilities with application in several practical problem solving tasks. The former are probabilities represented through intuitionistic fuzzy numbers, to indicate the uncertainty of the membership and nonmembership degrees in the value assigned to probabilities. Moreover, a dual hesitant fuzzy set (DHFS) is an extension of...

In this paper, two generalized hesitant fuzzy generalized Shapley-Choquet integral operators are defined, which globally consider the importance of elements in a set, and the correlations among them. Some important special cases are examined. An improvement order relationship between hesitant fuzzy elements (HFEs) is introduced, and a new distance measure of HFSs is defined. This distance measu...

In this paper, motivated by the ideas of dependent weighted aggregation operators, we develop some new hesitant fuzzy dependent weighted aggregation operators to aggregate the input arguments taking the form of hesitant fuzzy numbers rather than exact numbers, or intervals. In fact, we propose three hesitant fuzzy dependent weighted averaging(HFDWA) operators, and three hesitant fuzzy dependent...

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic and geometric aggregation operators with interval-valued dual hesitant fuzzy linguistic information. Then, motivated by the ideal of traditional arithmetic operation, we have developed some aggregation operators for aggregating interval-valued dual hesitant fuzzy linguistic information: i...

This paper presents new approach Hesitant Fuzzy K-nearest neighbour (HFK-nn) based document classification and numerical results analysis. The proposed classification Hesitant Fuzzy K-nearest neighbour (HFKnn) approach is based on hesitant Fuzzy distance. In this paper we have used hesitant Fuzzy distance calculations for document classification results. The following steps are used for classif...

This paper presents a general framework for the study of rough fuzzy sets in which fuzzy sets are approximated in a crisp approximation space. By the constructive approach, a pair of lower and upper generalized rough fuzzy approximation operators is first defined. The rough fuzzy approximation operators are represented by a class of generalized crisp approximation operators. Properties of rough...