基于前景理论的三角犹豫模糊多属性决策方法

针对属性权重信息完全未知,属性值为三角犹豫模糊元的多属性决策问题,提出一种基于前景理论和模糊结构元的决策分析方法。首先,基于模糊结构元理论,定义三角犹豫模糊元的结构元形式和海明距离公式,并通过求解属性间距离离差最大化的优化模型确定权重。其次,依据前景理论,分别以正负理想点作为决策参照点,构建收益矩阵和损失矩阵。在此基础上,应用TOPSIS方法计算各备选方案的相对贴近度,并依据相对贴近度的大小实现备选方案排序。最后,通过算例验证方法是有效和可行的。

Multiple Attribute Decision Making Method for HesitantTriangular Fuzzy Based on Prospect Theory

For multiple attribute decision making problems, in which the attribute weights are unknown completely and attribute values are in the form of hesitant triangular fuzzy element, the decision making method based on the prospect theory and fuzzy structured element is proposed. Firstly, according to the fuzzy structured element theory, the structured element form and Hamming distance formula of hesitant triangular fuzzy element are defined. Then, an optimization model based on the distance deviation of attribute values is constructed and the weight vector of attributes is obtained through solving the model. Furthermore, based on the main idea of prospect theory, the positive-ideal point and negative-ideal point are regarded as the reference points. And the income matrix and loss matrix are constructed respectively. Moreover, according to the method of TOPSIS, the relative closeness of each scheme is calculated to rank the alternatives. Finally, a numerical example is provided to illustrate the validity and feasibility of the proposed method.