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In the consensus reaching process (CRP), decision-makers (DMs) often present behaviors of tolerance and limited compromise when adjusting their opinions, which may lead to the actual decision deviating from the solution recommendation obtained by applying the current minimum cost consensus theory. In this paper, we propose a consensus-reaching approach based on maximum satisfaction under budget constraints for DMs with these two behaviors. To obtain a feasible budget constraint of the CRP, a reference budget consensus model (RBCM) incorporating both of these behaviors is first developed. Under the constraint of the limited budget, we propose a maximum satisfaction consensus model (MSCM) to maximize the satisfaction level of all DMs based on the goal programming theory. To further achieve different levels of consensus, we propose a soft MSCM under a certain threshold using soft …