© 2020, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.This study aims to propose the concept of intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices) and to present several of its basic properties. Therefore, it would be possible to improve the problem-modelling capabilities of the available intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets in the occurrence of a large number of data. Moreover, by using ifpifs-matrices, we suggest a new soft decision-making method, denoted by EA20, and apply it to a multi-criteria group decision-making (MCGDM) problem. We then compare the ranking performance of EA20 for five noise-removal filters with those of ten state-of-the-art soft decision-making methods. The results show that EA20 successfully models performance-based value assignment problems. Finally, we discuss ifpifs-matrices and EA20 for further research.