Search

This paper develops a single-granulation hesitant fuzzy rough set (SGHFRS) model from the perspective of granular computing. In the multi-granulation framework, we propose two types of multi-granulation rough sets model called the optimistic multi-granulation hesitant fuzzy rough sets (OMGHFRSs) and pessimistic multi-granulation hesitant fuzzy rough sets (PMGHFRSs). In the models, the multi-granulation hesitant fuzzy lower and upper approximations are defined based on multiple hesitant fuzzy tolerance relations. The relationships among the SGHFRSs, OMGHFRSs and PMGHFRSs are also established. In order to further measure the uncertainty of multi-granulation hesitant fuzzy rough sets (MGHFRSs), the concepts of rough measure and rough measure about the parameters α and β are presented and some of their interesting properties are examined. Finally, we give a decision-making method based on the MGHFRSs, and the validity of this approach is illustrated by two practical applications. Compared with the existing results, we also expound its advantages. [ABSTRACT FROM AUTHOR]

Through a combination of hesitant fuzzy sets with rough sets, this study develops a single-granulation hesitant fuzzy rough set model from the perspective of granular computing. In the multi-granulation framework, we propose two types of multi-granulation rough set model, called the optimistic multi-granulation hesitant fuzzy rough sets and pessimistic multi-granulation hesitant fuzzy rough sets. In the models, the multi-granulation hesitant fuzzy lower and upper approximations are defined based on multiple hesitant fuzzy tolerance relations. The relationships among the single-granulation hesitant fuzzy rough sets, optimistic multi-granulation hesitant fuzzy rough sets and pessimistic multi-granulation hesitant fuzzy rough sets are also investigated. Finally, we develop an approximation reduction approach of multi-granulation hesitant fuzzy rough sets to eliminate redundant hesitant fuzzy granulations with a detailed example. [ABSTRACT FROM AUTHOR]

The dual hesitant fuzzy soft set is a generalized soft set by combining the dual hesitant fuzzy set and the soft set. Rough set theory is a powerful mathematical tool for dealing with uncertainty. Using a rough set theory, this paper develops a rough set approach to dual hesitant fuzzy soft set based on decision making problems. Firstly, by employing a dual hesitant fuzzy compatible relation, a new rough set model, called dual hesitant fuzzy compatible rough set, is first proposed, and some fundamental properties of this model are further examined. Then the concepts of roughness measure and approximate precision of a crisp set in dual hesitant fuzzy compatible approximation space are introduced and their basic properties are discussed. Furthermore, we present a rough set approach to dual hesitant fuzzy soft set based on decision making. Meanwhile, an example is provided to show the validity of this approach in dual hesitant fuzzy soft set based on decision making problems. Finally, by comparing the novel method with the decision making method based on intuitionistic fuzzy soft sets, we point out some advantages of the novel method. [ABSTRACT FROM AUTHOR]

In this paper, we establish a systematic framework for the study of hesitant fuzzy compatible rough sets by a constructive approach. In the constructive approach, we introduce the concept of lower and upper hesitant fuzzy compatible rough approximation operators and also investigate some properties of this model. Then the concepts of roughness measure and approximate precision of a crisp set in hesitant fuzzy compatible approximation space are proposed and their basic properties are further discussed. Based on the hesitant fuzzy compatible rough sets, a novel decision-making approach to hesitant fuzzy soft sets is established. Meanwhile, a practical example is provided to demonstrate the effectiveness of this method. Finally, by comparing the novel method with the decision making method based on fuzzy soft sets, we point out some advantages of the novel method. [ABSTRACT FROM AUTHOR]