Conflict analysis in intelligent decision making has received increasing attention in recent years. However, few researchers have analyzed conflicts by considering trustworthiness from the perspective of common agreement and common opposition. Since L-fuzzy three-way concept lattice is able to describe both the attributes that objects commonly possess and the attributes that objects commonly do not possess, this paper introduces an L-fuzzy three-way concept lattice to capture the issues on which agents commonly agree and the issues which they commonly oppose, and proposes a hybrid conflict analysis model. In order to resolve conflicts identified by the proposed model, we formulate the problem as a knapsack problem and propose a method for selecting the optimal attitude change strategy. This strategy takes into account the associated costs and aims to provide the decision maker with the most favorable decision in terms of resolving conflicts and reaching consensus. To validate the effectiveness and feasibility of the proposed model, a case study is conducted, providing evidence of the model’s efficacy and viability in resolving conflicts.