Power average operators of linguistic intuitionistic fuzzy numbers and their application to multiple-attribute decision making

Linguistic intuitionistic fuzzy number (LIFN) is a special intuitionistic fuzzy number which can more easily describe the uncertainty and the vagueness information existing in the real world, and the power average (PA) operator can relieve some influences of unreasonable attribute values given by biased decision makers. In this paper, we will extend the PA operator to the LIFNs and propose some new operators, and develop some new decision making methods. Firstly, we introduce the definition, properties, score function, and operational rules of the LIFNs. Then, we propose some linguistic intuitionistic fuzzy power operators, such as linguistic intuitionistic fuzzy power averaging (LUTA) operator, linguistic intuitionistic fuzzy weighted power averaging (LIFWPA) operator, linguistic intuitionistic fuzzy power geometric (LIFPG) operator, linguistic intuitionistic fuzzy weighted power geometric (LIFWPG) operator, linguistic intuitionistic fuzzy generalized power averaging (LIFGPA) operator, linguistic intuitionistic fuzzy generalized weighted power averaging (LIFGWPA) operator. At the same time, we study some effective properties of these operators. Then, three methods based on the LIFWPA operator, LIFWPG operator and LIFGWPA operator for multi-attribute decision making are proposed. Finally, we use an illustrative example to demonstrate the practicality and effectiveness of the proposed methods.