Consistency analysis and priority derivation of triangular fuzzy preference relations based on modal value and geometric mean
Consistency analysis and priority derivation of triangular fuzzy preference relations based on modal value and geometric mean
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基于模态值和几何平均数的三角模糊偏好关系一致性分析及优先级推导
DOI：
10.1016/j.ins.2015.03.074
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发表时间：
2015-09
影响因子：
8.1
通讯作者：
Zhou-Jing Wang
中科院分区：
文献类型：
--
作者：
Zhou-Jing Wang
三角模糊偏好关系（TFPR）是一种有效的模型框架，两两估计不精确和简洁。为了得到可靠合理的决策结果，研究TFPR的一致性和优先级推导是非常重要的。本文分析了现有的一致TFPR的定义和性质，并说明了它们不具有关于决策方案排列的不变性。提出了一种新的基于三角模糊算法的传递性方程来定义相容的TFPR。新的传递性方程反映了三角模糊估计的模态值乘性一致性和几何平均乘性一致性。给出了一致TFPR的一些性质，并提出了TFPR的可接受一致性的概念。设计了基于几何均值和不确定性比的转换公式，将归一化三角模糊乘性权重转换为一致的TFPR。进一步建立了一个对数最小二乘模型，用于从具有可接受一致性的TFPR中导出归一化三角模糊乘性权向量。提出了一种基于几何平均值的三角模糊乘性权重比较和排序方法。三个数值例子，包括一个群体决策问题进行了检查，以证明所提出的模型的有效性和优势。
Triangular fuzzy preference relation (TFPR) is an effective framework to model pairwise estimations with imprecision and vagueness. In order to obtain a reliable and rational decision result, it is important to investigate consistency and priority derivation of TFPRs. The paper analyzes existing definitions and properties of consistent TFPRs, and illustrates that they have no invariance with respect to permutations of decision alternatives. A new triangular fuzzy arithmetic based transitivity equation is introduced to define consistent TFPRs. The new transitivity equation reflects multiplicative consistency of modal values and multiplicative consistency of geometric means of triangular fuzzy estimations. Some properties are presented for consistent TFPRs, and a notion of acceptable consistency is put forward for TFPRs. Geometric mean and uncertainty ratio based transformation formulae are devised to convert normalized triangular fuzzy multiplicative weights into consistent TFPRs. A logarithmic least square model is further established for deriving a normalized triangular fuzzy multiplicative weight vector from a TFPR with acceptable consistency. A geometric mean based method is developed to compare and rank triangular fuzzy multiplicative weights. Three numerical examples including a group decision making problem are examined to demonstrate validity and advantages of the proposed models.
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