Some Hybrid Geometric Aggregation Operators with 2-tuple Linguistic Information and Their Applications to Multi-attribute Group Decision Making

A new method is developed to solve multi-attribute group decision making (MAGDM) problem in which the attribute values, attribute weights and expert weights are all in the form of 2-tuple linguistic information. First, the operation laws for 2-tuple linguistic information are defined and the related properties of the operation laws are studied. Then, some new hybrid geometric aggregation operators with 2-tuple linguistic information are developed, involving the 2-tuple hybrid weighted geometric average (THWAG) operator, the 2-tuple hybrid linguistic weighted geometric average (T-HLWG) operator and the extended 2-tuple hybrid linguistic weighted geometric average (ET-HLWG) operator. These hybrid geometric aggregation operators generalize the existing 2-tuple linguistic geometric aggregation operators and reflect the important degrees of both the given 2-tuples and the ordered positions of the 2-tuples. In the proposed decision method, using the ET-HLWG operators the individual overall preference values of the alternatives are integrated into the collective ones of the alternatives, which are used to rank the alternatives. The method can sufficiently consider the importance degrees of different experts and thus relieve the influence of those unfair arguments on the decision results. A real example of evaluating university faculty is given to illustrate the proposed method and the comparison analysis demonstrates the universality and flexibility of the proposed method in this paper.