Group Role Three-Way Assignment for Managing Uncertainty in Role Negotiation

Role-based collaboration (RBC) is an innovative collaborative approach designed to enhance collaboration. Role negotiation (RN) is a critical step in RBC, during which the role set and the number of agents required for each role, i.e., role requirements, are determined. This process establishes the foundational input for group role assignment (GRA), where roles are assigned to agents to optimize group performance. Uncertainties in RN, such as task volume fluctuations, create dynamic agent requirements. However, existing RBC models typically assume RN to be static, thus failing to adequately address the substantial challenges. Three-way decision (3WD) is a robust decision-making methodology well-suited for managing uncertainty. To address the uncertainties in role requirements, this article introduces truncated discrete distribution to quantify role requirements, and presents a novel group role three-way assignment (GR3A) model. Compared with traditional RBC, our model offers an additional variable partial substitute choice that offers agents little salary during nonengagement periods but can transition to full involvement as required according to the prior agreement. GR3A is a dual-objective nonlinear optimization problem, for which a linearization strategy is proposed to achieve the optimal resolution. Additionally, sufficient and necessary conditions for these assignment problems are put forward to enhance the efficacy of the proposed solutions. To our knowledge, this study innovatively introduces a truncated discrete distribution and 3WD into the RBC framework. Empirical validation through simulations demonstrates the effectiveness and efficacy of the proposed method within the RBC context.