Abstract: A method of random lattice order decision analysis based on interval-valued distribution preference vector by entropy theory is proposed, focused on decision preference system with preference relations' belief degree described by interval-value. First, the preference characterization of decision makers is extended from four variety relations to seven variety preference relations, combined with the concept and property of interval evidence, the concept and property of interval-valued distribution preference vector and relative entropy on the lattice order preference system are given. Then the ER nonlinear optimization model based on preference entropy is established, the individual preferences are aggregated by applying the priority rules and intersection rule, and the specific steps of the decision making are qiven. The feasibility and effectiveness of the approach proposed in this paper are illustrated with a numerical example.

Key words: group decision-making, lattice order preference, interval belief degree, preference entropy, nonlinear optimization

摘要： 针对偏好优劣关系的信度为区间值的决策偏好系统,运用熵理论提出了一种基于区间值分布偏好向量的决策分析方法。首先,将决策者对方案的偏好描述由:优于、劣于、等价和不可比这四种关系拓广为优于、劣于、等价、无法比较但有上确界、无法比较但有下确界、无法比较且有上确界又下确界、不可比七种偏好关系,并结合区间证据的概念和性质给出了决策偏好系统的区间值分布偏好向量与相对熵的概念、性质。然后,构建了基于偏好熵的证据推理非线性优化模型,通过求解模型,并结合优先原则和集结规则将个人偏好集结成群体偏好,给出了该决策方法的具体步骤,举例说明了方法的可行性。

关键词: 群决策, 格序偏好, 区间信度, 偏好熵, 非线性优化模型