Minimum cost consensus modelling under various linear uncertain-constrained scenarios

Abstract Group decision-making combined with uncertainty theory is verified as a more conclusive theory, by building a bridge between deterministic and indeterministic group decision-making in this paper. Due to the absence of sufficient historical data, reliability of decisions are mainly determined by experts rather than some prior probability distributions, easily leading to the problem of subjectivity. Thus, belief degree and uncertainty distribution are used in this paper to fit individual preferences, and five scenarios of uncertain chance-constrained minimum cost consensus models are further discussed from the perspectives of the moderator, individual decision-makers and non-cooperators. Through deduction, reaching conditions for consensus and analytic formulas of the minimum total cost are both theoretically given. Finally, with the application in carbon quota negotiation, the proposed models are demonstrated as a further extension of the crisp number or interval preference-based minimum cost consensus models. In other words, the basic conclusions of the traditional models are some special cases of the uncertain minimum cost consensus models under different belief degrees.