Multiple Attribute Decision Making Method Based on the Trapezoid Fuzzy Linguistic Hybrid Harmonic Averaging Operator

A new method is proposed to solve the multiple attribute decision making (MADM) problems with the trapezoid fuzzy linguistic variables ( Vs TFL ) based on the trapezoid fuzzy linguistic hybrid harmonic averaging (TFLHHA ) operator. To begin with, this paper reviews the concept and operational rules of the Vs TFL , the calculation method of the possibility degree with Vs TFL , and the comparison method of Vs TFL . Then, some operators are proposed, in order to aggregate the Vs TFL , such as the trapezoid fuzzy linguistic weighted harmonic averaging (TFLWHA ) operator, the trapezoid fuzzy linguistic ordered weighted harmonic averaging ( TFLOWHA ) operator, and the trapezoid fuzzy linguistic hybrid harmonic averaging ( ) TFLHHA operator. Furthermore, based on the TFLHHA operator, a new method solving the MADM problems with the Vs TFL is proposed. Finally, an illustrative example is given to show the decision making steps, and it verifies the effectiveness of the developed method.