语言多属性决策的目标规划模型
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Goal programming models for multiple attribute decision making under linguistic setting
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    摘要:

    研究了只有部分属性权重信息、属性值以语言变量或不确定语言变量形式给出且决蓑者对方案有偏好信息的语言多属性决策问题.给出了语言变量和不确定语言变量的运算法则,以及不确定语言变量之间比较的可能度公式,定义了语言变量的偏离度概念.在属性值以1)语言变量和2)不确定语言变量,这两种形式给出的情形下,分别建立了一个基于偏离度的目标规划模型,并通过求解这两种模型分别获得相应的属性权重.然后对于情形1),利用语言加权平均(LWA)算子,对语言决策信息进行加权集成,继而对方案进行排序和择优;对于情形2),利用不确定语言加权平均(ULWA)算子,对不确定语言决策信息进行加权集成,并利用可能度公式构造可能度矩阵(互补判断矩阵),继而利用互补判断矩阵排序公式对决策方案进行排序和择优.最后进行了实例分析

    Abstract:

    In this paper, we study the multiple attribute decision making problems, in which the information about attribute weights is partly known and the attribute values take the form of linguistic variables or uncertain linguistic variables, and the decision maker has preferences on alternatives. We introduce the operation laws of linguistic variables and uncertain linguistic variables and a formula of possibility degree for the comparison between uncertain linguistic variables, and then define the concept of deviation degree between linguistic variables. We establish two goal programming models based on the concept of deviation degree under the situations where the attribute values are linguistic variables and uncertain linguistic variables respectively. By solving these two models, the attribute weights can be obtained. After that, when the attribute values are linguistic variables, we utilize the linguistic weighted averaging (LWA) operator to aggregate the given linguistic decision information, and then rank the ahematives and select the most desirable one(s); when the attribute values are uncertain linguistic variables, we utilize the uncertain linguistic weighted averaging (ULWA) operator to aggregate the given uncertain linguistic decision information and utilize the formula of possibility degree to construct a possibility degree matrix (or called complementary judgement matrix), and then utilize the priority formula of complementary judgement matrix to rank the alternatives and to select the most desirable one(s). Finally, an illustrative example is also given

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徐泽水.语言多属性决策的目标规划模型[J].管理科学学报,2006,9(2):

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