In this paper we develop a new method for 2-tuple linguistic multiple attribute decision making, namely the 2-tuple linguistic generalized ordered weighted averaging distance (2LGOWAD) operator. This operator is an extension of the OWA operator that utilizes generalized means, distance measures and uncertain information represented as 2-tuple linguistic variables. By using 2LGOWAD, it is possible to obtain a wide range of 2-tuple linguistic aggregation distance operators such as the 2-tuple linguistic maximum distance, the 2-tuple linguistic minimum distance, the 2-tuple linguistic normalized Hamming distance (2LNHD), the 2-tuple linguistic weighted Hamming distance (2LWHD), the 2-tuple linguistic normalized Euclidean distance (2LNED), the 2-tuple linguistic weighted Euclidean distance (2LWED), the 2-tuple linguistic ordered weighted averaging distance (2LOWAD) operator and the 2-tuple linguistic Euclidean ordered weighted averaging distance (2LEOWAD) operator. We study some of its main properties, and we further generalize the 2LGOWAD operator using quasi-arithmetic means. The result is the Quasi-2LOWAD operator. Finally we present an application of the developed operators to decision-making regarding the selection of investment strategies.