The present work is focused on multi-attribute group decision-making (MAGDM) problems with the uncertain 2-tuple linguistic information (ULI 2-tuple ) based on new aggregation operators which can capture interrelationships of attributes by a parameter vector P. To begin with, we present some new uncertain 2-tuple linguistic MM aggregation (UL 2-tuple -MM) operators to handle MAGDM problems with ULI 2-tuple , including the uncertain 2-tuple linguistic Muirhead mean (UL 2-tuple -MM) operator, uncertain 2-tuple linguistic weighted Muirhead mean (UL 2-tuple -WMM) operator. In addition, we extend UL 2-tuple -WMM operator to a new aggregation operator named extended uncertain 2-tuple linguistic weighted Muirhead mean (EUL 2-tuple -WMM) operators in order to handle some decision-making problems with ULI 2-tuple whose attribute values are expressed in ULI 2-tuple and attribute weights are also 2-tuple linguistic information. Whilst, the some properties of these new aggregation operators are obtained and some special cases are discussed. Moreover, we propose a new method to solve the MAGDM problems with ULI 2-tuple . Finally, a numerical example is given to show the validity of the proposed method and the advantages of proposed method are also analysed.