Picture uncertain linguistic aggregation operators and their application to multiple attribute decision making

In this paper, we investigate the multiple attribute decision making problems with picture uncertain linguistic information. Then, we utilize arithmetic and geometric operations to develop some picture uncertain linguistic aggregation operators: picture uncertain linguistic weighted average (PULWA) operator, picture uncertain linguistic weighted geometric (PULWG) operator, picture uncertain linguistic ordered weighted average (PULOWA) operator, picture uncertain linguistic ordered weighted geometric (PULOWG) operator, picture uncertain linguistic hybrid average (PULHA) operator and picture uncertain linguistic hybrid geometric (PULHG) operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the picture uncertain linguistic multiple attribute decision making problems. Finally, a practical example for micro-credit risk evaluation of micro-credit companies is given to verify the developed approach and to demonstrate its practicality and effectiveness.