Trapezoid fuzzy 2-tuple linguistic aggregation operators and their applications to multiple attribute decision making

In this paper, we investigate the multiple attribute decision making (MADM) problems in which the attribute values take the form of trapezoid fuzzy 2-tuples. Firstly, we develop some trapezoid fuzzy 2-tuple linguistic aggregation operators based on the operational laws of trapezoid fuzzy 2-tuples, such as the trapezoid fuzzy 2-tuple weighted geometric (TFTWG) operator, the trapezoid fuzzy 2-tuple ordered weighted geometric (TFTOWG) operator, the generalized trapezoid fuzzy 2-tuple weighted average (GTFTWA) operator and the generalized trapezoid fuzzy 2-tuple ordered weighted average (GTFTOWA) operator. Then, we study some desirable properties of the developed operators, such as idempotency, monotonicity, commutativity and boundedness, and analyze some special cases of these operators. Furthermore, we propose an approach to multiple attribute decision making under trapezoid fuzzy linguistic environment based on the GTFTWA and TFTWG operators. Finally, an illustrative example is given to verify the proposed approach and to demonstrate its practicality and effectiveness.