Construction of Role Assigning Lattice

Agent organization is a set of agents to solve a problem together, it describes the relationship between agents and roles which agents taking. Firstly, this paper proposes the concept of stable matching in role assigning, and constitutes all the stable matching into a set F, then describes its properties. Secondly, considering the preference of role and agent, we construct a strong stable relations, so stable matching set F and strong stable relation les constitute a partial order structure <F, les>. At last, two operators join operator otimes and meet operator otimes on the partial order structure are constructed. Due to closure of these operators, algebra structure <F, oplus, otimes is a lattice which is called role assigning lattice. After Constructed role assigning lattice, it has laid a solid foundation for the formation and evolution of agent organization.