Multi-attribute decision-making algorithms are well-suited to solve portfolio selection problems. Experts might have to consider particular parts of the issue in certain situations, leading to incomplete preferences. In this study, we have provided an additive consistency definition represented by a Fermatean fuzzy priority vector. We will present a model for generating missing judgments in incomplete Fermatean fuzzy preference relations and the property of the suggested concept of additive consistency. In recent years, the development of information technology has enabled social networks to be online communication platforms for individuals to exchange messages and share information. This enhanced communication environment leads to a new format of group decision-making that acknowledges the influence of the social relationships among experts on the decision process and results. Our research has developed a social network group decision-making framework using incomplete Fermatean fuzzy preference relations to address portfolio investment selection issues, especially when multiple decision-makers are involved.