Concrete, one of the sources of energy consumption and carbon emissions, is widely used in the construction industry. The selection of concrete materials raises the question of energy sustainability and turns it into a complex multicriteria decision-making (MCDM) issue. To address this, we present an MCDM framework based on the intuitionistic linguistic hybrid weighted logarithmic averaging distance (ILHWLAD). To begin with, the intuitionistic linguistic numbers are used to deal with the uncertainty and fuzziness of the decision-making process. In addition, in view of the significance and the ordered position of the input arguments, an intuitionistic linguistic hybrid weighted logarithmic averaging distance (ILHWLAD) operator is defined. We, then, initiate the criteria system and present the MCDM framework based on the ILHWLAD to select the finest concrete. A case study involving four alternative materials, namely, autoclaved aerated concrete (AAC), hollow concrete blocks (HCB), expanded polystyrene (EPS), and lime hemp concrete (LHC), is presented to verify the scientificity of the framework.