The semantic gap between formal software protocols and designs is one of the major problems restricting smooth transfer of a formal method from protocols towards designs. Goal operationalization is an essential approach to address this issue. KAOS is one of the main protocol languages supporting goal operationalization. However, agents, goals and operations provided in KAOS lack for unified semantic descriptions. In this paper, we propose an agent model, which can unify the operations on agent structure (state) and events of BDI Model, and extend their syntax and semantics. An advanced Goal Operationalized Protocol Model (GOP Model) is built to unify the descriptions of agents, goals and operations. Using a dual agent, we can describe the operation as an operator in the state relationship between an agent and a dual agent. We set up a structure model of the agent attribute field based on a multi-sorted algebra, which can join an operator described in GOP Model with structure properties of the sublevel attribute fields. Therefore, the operation model of a single field atom can be adopted to deal with the goal operation of all atoms in an attribute field. Our work is demonstrated to be theoretically significant and practically valuable.