Some Power Aggregation Operators for Hesitant Intuitionistic Fuzzy Linguistic Set and Their Applications to Multiple Attribute Decision Making

Abstract

With respect to multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant intuitionistic fuzzy linguistic elements (HIFLEs) and the attributes are interdependent, this paper investigates a novel MADM method with hesitant intuitionistic fuzzy linguistic information. Firstly, some hesitant intuitionistic fuzzy linguistic power aggregation operators are developed based on the operational laws of HIFLEs and power aggregation operators, such as hesitant intuitionistic fuzzy linguistic power average (HIFLPA) operator, hesitant intuitionistic fuzzy linguistic power geometric (HIFLPG) operator, hesitant intuitionistic fuzzy linguistic weighted power average (HIFLWPA) operator and hesitant intuitionistic fuzzy linguistic weighted power geometric (HIFLWPG) operator. Then, some desirable properties of these operators and the relationships between them are discussed in detail. Furthermore, based on the HIFLWPA operator, an approach to MADM is proposed under hesitant intuitionistic fuzzy linguistic environment. Finally, a numerical example is given to illustrate the application of the proposed method.