2-Tuple linguistic hybrid arithmetic aggregation operators and application to multi-attribute group decision making

The focus of this paper is on multi-attribute group decision making (MAGDM) problems in which the attribute values, attribute weights, and expert weights are all in the form of 2-tuple linguistic information, which are solved by developing a new decision method based on 2-tuple linguistic hybrid arithmetic aggregation operator. First, the operation laws for 2-tuple linguistic information are defined and the related properties of the operation laws are studied. Hereby some hybrid arithmetic aggregation operators with 2-tuple linguistic information are developed, involving the 2-tuple hybrid weighted arithmetic average (THWA) operator, the 2-tuple hybrid linguistic weighted arithmetic average (T-HLWA) operator, and the extended 2-tuple hybrid linguistic weighted arithmetic average (ET-HLWA) operator. In the proposed decision method, the individual overall preference values of alternatives are derived by using the extended 2-tuple weighted arithmetic average operator (ET-WA). Utilized the ET-HLWA operator, all the individual overall preference values of alternatives are further integrated into the collective ones of alternatives, which are used to rank the alternatives. A real example of personnel selection is given to illustrate the developed method and the comparison analyses demonstrate the universality and flexibility of the method proposed in this paper.