In this work, ambiguity and unclarity are coped with the effective tools of picture fuzzy sets (PFSs), especially where the conditions demand simulation of various dimensions for evaluation, for example, decision making. PFS requires operators to measure the coordination of two PFSs. As far as this article is concerned, we bring new operators to PFSs with an application, validating this as the generalization of the concept of fuzzy sets and intuitionistic fuzzy sets. The hybrid structure of PFSs has been incorporated with other operators to develop picture fuzzy Dombi Hamy mean operator, picture fuzzy weighted Dombi Hamy mean operator, picture fuzzy Dombi dual Hamy mean operator, and picture fuzzy weighted Dombi dual Hamy mean operator. Further, the properties such as idempotency, monotonicity, boundedness, and commutativity related to each proposed operator have been discussed. By using these operators, the multiple attribute group decisionmaking methods are proposed. Moreover, we have explained the application by providing an example of a car supplier. The results are concluded by selecting the best car on the basis of attributes such as quality, production, service efficiency, and risk factors using operators defined on PFSs. A comparative study is also conducted to study the significance of the developed work.