Abstract:

With respect to emergency decision-making problem with unknown attribute weights and interval-valued Pythagorean fuzzy linguistic numbers, a multi-stage multi-attribute decision-making method based on combination weighting and prospect theory is proposed. The attribute weights ranges are determined by the information entropy of alternative, and attribute weights are determined by solving an optimization model with minimum interval-valued Pythagorean fuzzy entropy. The positive and negative ideal points are defined as the reference points, the prospect values of each stage and each state are calculated by using prospect theory, and the prospect values of alternative chains are obtained considering the influence of the previous stage on the state probability of the next stage. A multi-objective optimization model is established to achieve the goal of maximum prospect value and minimum cost of the alternative chain, meanwhile, the multi-objective is converted into a single objective, and the optimal alternative of each stage is determined by solving the optimization model. The feasibility of the method is verified by an example of epidemic prevention and control, and the validity of the method is illustrated by comparing the effect of multi-stage decision-making with that of a single stage.

Key words: interval-valued Pythagorean fuzzy, combination weighting, prospect theory, alternative chain, epidemic

摘要：

针对属性权重未知且决策信息为区间Pythagorean模糊语言的应急决策问题，提出一种基于组合赋权和前景理论的多阶段多属性决策方法。根据方案信息熵确定属性权重范围，并以区间Pythagorean模糊熵最小为目标构建模型并求解，以确定属性权重。定义正负理想点作为参考点，运用前景理论求出每一阶段各状态下的前景值，并考虑前一阶段方案对后一阶段状态概率的影响，求出方案链的前景值。在此基础上，以方案链的前景值最大和成本最小为目标构建优化模型，并将多目标转化为单目标，求解模型以确定各阶段的最优方案。以某传染病疫情防控应急决策问题为算例验证了该方法的可行性，并将多阶段决策效果与单一阶段的决策结果进行比较分析，验证了该方法的有效性。

关键词: 区间Pythagorean模糊, 组合赋权, 前景理论, 方案链, 流行病