The selection of an appropriate technology transfer (TT) method is a complex multidimensional problem, which involves a multitude of situational qualitative and quantitative criteria. Despite multiple classifications and effective practices, expert opinion is still essential for every case. The complexity and dependence of TT method selection on human judgment have led to an increase in the application and integration of Multi-Criteria Group Decision-Making (MCGDM) methods, as well as fuzzy and gray systems theories, to address uncertainties related to data collection and selection of TT methods and criteria. The present study contributes to this trend by presenting a novel integrated Shannon-Projection Attribute Function (PAF) method, based on three-parameter interval gray numbers and describes its application in TT methods for the building industry. To calculate the weight of the assessment criteria, selected based on the literature review and Delphi panel, Shannon entropy can reduce uncertainties associated with the weighting criteria. Furthermore, three-parameter interval gray numbers can reduce uncertainties related to expert appraisal. In this study, we used the PAF method to rank TT methods. Also, we presented a brief analysis of the method application in the building industry. The results showed that reverse engineering and import of capital goods and machinery are the best TT methods, respectively.