DEMATEL exhibits a relational representation of variables and their interdependence. Impact Relations Map (IRM), a visual tool and the end product of DEMATEL, readily provides valuable insight into the influence of variables and facilitates to deal with complex decision problems. Acquiring a proper threshold value and a reasonable IRM consecutively is essential for correct relational evaluation of cause and effect variables. The methods available in the literature to find a DEMATEL threshold value have been implemented and tried, but no successful results have been obtained with the problem of interest. Therefore, we develop and introduce a new method, Constricted Information Space (CIS), to attain this goal. The method ensures a threshold value that not only neglects unnecessary relations but also retains enough relational information crucial for the researcher. Furthermore, DEMATEL-Based Analytic Network Process (DANP), a hybrid model, is employed for weighing and ranking the evaluation criteria of Hi-Fi audio systems. Numerical and visual comparisons of various threshold methods and their impacts on the final rankings are presented. The key criteria that emerged as a result of the study are disclosed for audiophiles to assess the audio quality of Hi-Fi audio systems. (C) 2022 Elsevier Ltd. All rights reserved.