基于区间概率偏好的随机格序群决策方法

为解决偏好优劣关系具有随机性,且随机事件的概率采用区间值描述的随机格序群体决策问题,提出了一种基于专家偏好服从某种区间概率分布的决策方法.将决策者对方案的偏好描述由优于、劣于、等价和不可比4种关系拓展为优于、劣于、等价、无法比较但有上确界、无法比较但有下确界、无法比较但既有上确界又有下确界、不可比7种偏好关系,并结合区间概率的概念、性质和区间数的运算规则,定义了格上偏好关系的概率分布.然后确定方案对偏好关系的概率最大化目标函数,结合优先原则和集结规则,将个人偏好集结成群体偏好.最后,通过案例给出该决策方法的具体步骤,说明了该方法的可行性.

Random Lattice Order Group Decision-Making Based on Interval Probability Preferences

To solve the random lattice order group decision-making problems where preference relations are random and probability of random events is described by interval values,a decision-making method based on the preferences of decision makers subject to an interval probability distribution is proposed.First,the preference relations are extended from four kinds(preference,inferior,indifference,and incomparability) to seven kinds(preference,inferior,indifference,incomparability,incomparability with a minimum upper bound,incomparability with a maximum lower bound,and incomparability with a minimum upper bound and a maximum lower bound).Second,the probability distribution of lattice order preference relations is defined on the basis of the concept and property of interval probability,and the operation rules of interval numbers.Third,the probability maximization objective function of preference relation of any pair of alternatives is established,and individual preferences are aggregated to group preferences according to priority rules and intersection rules.Finally,the steps of the group decision-making method are listed through a case study,and the feasibility and effectiveness of the method is validated.