Abstract: This paper presents a multi-attribute sorting method applied to problem whose information on weights is partly known and attribute values are interval intuitionistic fuzzy numbers. The method is based on prospect theory and quantum evolution algorithm. According to prospect theory and fuzzy numbers’ distance formula, it defines interval intuitionistic fuzzy numbers’ prospect value function. Meanwhile, it brings decision makers’ risk preference of project into decision-making behavior. The nonlinear programming model based on projects’ comprehensive prospect value maximization can be constructed. By putting quantum evolution algorthm, the optimal weight vector of model can be solved. The projects’ comprehensive prospect values determine the order. This method is applied to fuzzy decision making environment, can meet decision makers who do not provide determining attribute weights, and fully consider risk psychological factor’s influence on decision behavior. Thus it has wide range of application value. At the end, a numerical example shows the effectiveness and feasibility of the method.

Key words: prospect theory, quantum evolution algorithm, interval intuitionistic fuzzy number, multi-attribute decision-making

摘要： 针对属性权重不完全确定且属性偏好值为区间直觉模糊数的多属性决策问题，提出一种基于前景理论和量子进化算法的模糊多属性决策方法。该方法根据前景理论及模糊数距离公式，定义区间直觉模糊数的前景价值函数，同时将决策者对方案的风险偏好纳入决策行为中，以此来构建方案综合前景值最大化的非线性规划模型。通过引入量子进化算法，求解模型得出最优权重向量。最终根据方案前景值确定出方案的排序。该方法适用于模糊决策环境，能满足决策者不提供确定属性权重的要求，并充分考虑决策者风险心理因素对决策行为的影响，具有广泛的应用价值。数值算例说明了该方法的有效性和可行性。

关键词: 前景理论, 量子进化算法, 区间直觉模糊数, 多属性决策