Linguistic Interval-Valued Atanassov Intuitionistic Fuzzy Sets and Their Applications to Group Decision Making Problems

In this paper, we propose the concept of a linguistic interval-valued Atanassov intuitionistic fuzzy set (LIVAIFS), whose membership and nonmembership degrees are represented by the interval-valued linguistic terms, for better dealing with imprecise and uncertain information during the decision-making process. In it, first some operational laws, score, and accuracy functions of LIVAIFS are defined with a brief study of related properties. Then, based on these operational laws, several aggregating operators are proposed to aggregate the linguistic interval-valued Atanassov intuitionistic fuzzy (LIVAIF) information. Some properties and inequalities are established to show the effectiveness and validity of proposed operators. Furthermore, a group decision making (GDM) approach, based on proposed operators, has been presented to solve the multiattribute GDM problems under LIVAIF environment. Finally, an illustrative example has been presented to demonstrate the approach.