Abstract
The difficulty of establishing a common membership degree is not because there is a margin of error or some possibility distribution values, but because there is a set of possible values. Based on hesitant fuzzy sets and soft sets, a hesitant soft fuzzy rough set model is proposed in this paper. Basic properties of hesitant soft fuzzy rough sets are investigated in detail. We obtain a decomposition theorem for a hesitant fuzzy binary relation, which states that every typical hesitant fuzzy binary relation on a set can be represented by a well-structured family of fuzzy binary relations on that set. Indeed, a hesitant fuzzy soft set can induce a hesitant fuzzy binary relation. Then we give the relationship between hesitant fuzzy rough sets and hesitant soft fuzzy rough sets. In addition, we prove a characterization theorem for the hesitant soft fuzzy rough set model, which shows that the lower and upper hesitant soft fuzzy rough approximations can be equivalently defined by using level sets of the hesitant fuzzy soft set. Finally, by analyzing the limitations and advantages in the existing literatures, we establish an approach to decision making problem based on the hesitant soft fuzzy rough set model proposed in this paper and give a practical example to illustrate the validity of the novel method.
Highlights
The contemporary concern about knowledge representation and information systems has put forward useful extensions of classical set theory such as fuzzy set theory and rough set theory
Both theories address the problem of information granulation: the theory of fuzzy sets is centred upon fuzzy information granulation, whereas the rough set theory is focused on crisp information granulation
Based on the decomposition theorem for a hesitant fuzzy binary relation, which states that every typical hesitant fuzzy binary relation on a set can be represented by a well-structured family of fuzzy binary relations on that set, we give the relationship between hesitant fuzzy rough sets and hesitant soft fuzzy rough sets
Summary
The contemporary concern about knowledge representation and information systems has put forward useful extensions of classical set theory such as fuzzy set theory and rough set theory. Torra [28] introduced the concept of hesitant fuzzy set (HFS) as an extension of the FS in which the membership degree of a given element, called the hesitant fuzzy element (HFE), is defined as a set of possible values This situation can be found in a group decision making problem. In 2011, Gong et al [8] introduced the interval-valued intuitionistic fuzzy soft set and described its application to multi-parameter group decision-making problems. The interval-valued hesitant fuzzy soft set, the weighted interval-valued hesitant fuzzy soft set and their applications in decision making problem were presented by Zhang et al [37]. In 2018, the hesitant fuzzy compatible rough set over two different universes and its application in hesitant fuzzy soft set based decision making were investigated by Zhang and He [40].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
