不完全确定信息的群体语言指派问题的求解方法

针对决策者权重和准则权重为不完全确定信息且评价语言值确定或位于二个标准语言值之间甚至缺失的多准则指派问题,提出了一种求解方法。首先利用证据推理算法计算得到各候选人完成各任务的优劣程度属于各个语言评价等级的信任度,并据此利用二元语义的Δ函数及其函数Δ-1将其集成为群体在所有准则下的综合评价矩阵,然后结合决策者权重和准则权重的不完全确定信息等构建非线性混合整数规则模型,并利用粒子群算法与匈牙利算法联合进行求解。最后实例说明该方法的可行性和有效性。

Method of Group Multi-Criteria Linguistic Assignment Problem with Incomplete Certain Information

For group multi-criteria assignment problems with linguistic assessment information,a new method based on evidential reasoning and two tuple is proposed,in which the decision-makers' weights and the evaluation criteria weights are incomplete certain,and the assessment information may be between two linguistic assessment grades or not be given by the decision makers. Firstly the evidential reasoning algorithm is applied to calculate the belief degree that any candidate accomplishes any task is belonging to any linguistic assessment grade. Secondly,according to the belief degree obtained above and with the function △ and △^-1 of two tuple,the original assessment matrices are aggregated into the synthetic efficiency matrix. The nonlinear mixed integral programming model is constructed based on the incomplete certain information of the decision makers'weights and criteria weights,and the model is worked out with the improved Particle Swarm Optimization Algorithm and Hungary Algorithm. Finally an example is given to show the feasibility and availability of this method.