The development of the FILA-SoS meta-architecture approach to acknowledged systems of systems (SoS) analysis allows a relatively unbiased method for exploring a potential SoS architecture space. This paper delves more deeply into the process of building the lists of desirable fuzzy attributes of a SoS, developing rules for combining attribute values to an overall assessment, and discovering membership function shapes that work well. A wide range of options exist for all the individual elements of SoS assessment. Some recommendations for finding an appropriate combination for the adjustable parameters of fuzzy assessment models through random architecture chromosome testing and iteration are developed.