To solve the multi-attribute group decision-making problem with Pythagorean fuzzy number as attribute value and unknown expert weights in social networks, a solution considered trust relationships is proposed. Firstly, the comprehensive weights of experts were calculated based on point degree centrality and proximity centrality after the experts' social network graph was charted. Secondly, the group decision matrix was obtained using the Pythagorean fuzzy weighted average operator, and the consensus levels of attribute values, options, and decision-makers were computed. Thirdly, a trust-based feedback mechanism was proposed to adjust the initial information that does not meet the threshold of consensus level. Finally, the comprehensive score values of each alternative were calculated using the Romanian selection method and the group score matrix, after which the alternatives were ranked. A numerical example shows that this method is feasible and effective, as it considers the trust relationships of decision-makers, optimizes the consensus process in group decision-making within social network environments, achieves a satisfactory level of group consensus, and preserves the initial judgment information of decision-makers to the greatest extent.