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The ordered weighted distance (OWD) measure developed by Xu and Chen having been proved suitable to deal with the situation where the input arguments are represented in exact numerical values. In this paper, we develop some new geometric distance measures with intuitionistic fuzzy information, which are the generalization of some widely used distance measures, including the intuitionistic fuzzy weighted geometric distance (IFWGD) measure, the intuitionistic fuzzy ordered weighted geometric distance (IFOWGD) measure, the intuitionistic fuzzy ordered weighted geometric Hamming distance (IFOWGHD) measure, the intuitionistic fuzzy ordered weighted geometric Euclidean distance (IFOWGED) measure, the intuitionistic fuzzy hybrid weighted geometric distance (IFHWGD) measure. These developed weighted geometric distance measures are very suitable to deal with the situation where the input arguments are represented in intuitionistic fuzzy values. And then, we present a consensus reaching process based on the developed distance measures with intuitionistic fuzzy preference information for group decision making. Finally, we apply the developed approach with a numerical example to group decision making under intuitionistic fuzzy environment. [ABSTRACT FROM AUTHOR]

In this paper, we develop some new aggregation operators with pure linguistic information including the uncertain pure linguistic weighted geometric mean (UPLWGM) operator, the induced uncertain pure linguistic ordered weighted geometric mean (IUPLOWGM) operator, and the induced uncertain pure linguistic hybrid geometric mean (IUPLHGM) operator. These developed aggregation operators are very suitable to deal with the situation where the input arguments are represented in uncertain pure linguistic variables. Also, as a more general type of aggregation operator, the IUPLHGM operator is based on the UPLWGM and IUPLOWGM operators, and it can reflect the importance degrees of both the given uncertain linguistic variables and their ordered positions. Moreover, in the situations where the information about all the attribute weights, the attribute values and the expert weights are expressed in the form of linguistic labels variables, we develop an approach based on the IUPLHGM operator for multiple attribute group decision making with pure linguistic information. Finally, an application of the developed approach to group decision making problem regarding the selection of investments is given. Also, we present a comparative analysis with other related decision making methods to demonstrate the effectiveness of the developed approach. [ABSTRACT FROM AUTHOR]