Hesitant Trapezoid Fuzzy Hamacher Aggregation Operators and Their Application 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 hesitant trapezoid fuzzy information. Firstly, inspired by the idea of hesitant fuzzy sets and trapezoid fuzzy numbers, the definition of hesitant trapezoid fuzzy set and some operational laws of hesitant trapezoid fuzzy elements are proposed. Then some hesitant trapezoid fuzzy aggregation operators based on Hamacher operation are developed, such as the hesitant trapezoid fuzzy Hamacher weighted average(HTr FHWA) operator, the hesitant trapezoid fuzzy Hamacher weighted geometric(HTr FHWG) operator, the hesitant trapezoid fuzzy Hamacher Choquet average(HTr FHCA), the hesitant trapezoid fuzzy Hamacher Choquet geometric(HTr FHCG),etc. Furthermore, an approach based on the hesitant trapezoid fuzzy Hamacher weighted average(HTr FHWA) operator and the hesitant trapezoid fuzzy Hamacher weighted geometric(HTr FHWG)operator is proposed for MADM problems under hesitant trapezoid fuzzy environment. Finally, a numerical example for supplier selection is given to illustrate the application of the proposed approach.