Consistency analysis and group decision making based on triangular fuzzy additive reciprocal preference relations
Consistency analysis and group decision making based on triangular fuzzy additive reciprocal preference relations
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基于三角模糊加性互惠偏好关系的一致性分析与群体决策
DOI：
10.1016/j.ins.2016.04.047
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发表时间：
2016-09
影响因子：
8.1
通讯作者：
Xiayu Tong
中科院分区：
文献类型：
--
作者：
Zhou-Jing Wang;Xiayu Tong
三角模糊数是对不精确和不确定信息进行建模的有效方法，在决策中得到了广泛的应用。利用交比表示的三元组刻画正三角模糊数，引入交比表示的三角模糊数(CRETFN)和三角模糊可加互反偏好关系(TFARPRs)的概念。给出了TFARPR与三角模糊乘法互反偏好关系之间的转换方法，给出了CRETFN的补、加、乘、幂等运算法则。建立了基于交比表示的三角模糊乘法传递性方程，定义了TFARPR的乘法一致性。新的一致性刻画了交比表示的模态值之间的Tanino乘法一致性，以及由交比表示的三角模糊判断的上下支撑值构成的区间模糊偏好关系的几何一致性。为乘性相容的TFARPR提供了一些理想的性质。我们提出了一种交叉比率表示的三角模糊加权几何算子来聚合CRETFN，并将其扩展到融合TFARPR。定义了得分和不确定性指数函数，并利用该函数设计了一种新的CRETFN比较方法。给出了用TFARPR解决群决策问题的具体步骤。文中给出了六个算例，验证了所提模型的有效性和适用性。
Triangular fuzzy numbers are effective in modeling imprecise and uncertain information, and have been widely applied in decision making. This paper uses a cross-ratio-expressed triplet to characterize a positive triangular fuzzy number, and introduces notions of cross-ratio-expressed triangular fuzzy numbers (CRETFNs) and triangular fuzzy additive reciprocal preference relations (TFARPRs). We present transformation methods between TFARPRs and triangular fuzzy multiplicative reciprocal preference relations, and develop operational laws of CRETFNs, such as complement, addition, multiplication and power. A cross-ratio-expressed triangular fuzzy multiplication based transitivity equation is established to define multiplicative consistency of TFARPRs. The new consistency captures Tanino's multiplicative consistency among the cross-ratio-expressed modal values, and geometric consistency of the interval fuzzy preference relation constructed from lower and upper support values of cross-ratio-expressed triangular fuzzy judgments. Some desirable properties are furnished for multiplicatively consistent TFARPRs. We propose a cross-ratio-expressed triangular fuzzy weighted geometric operator to aggregate CRETFNs, and extend it to fuse TFARPRs. Score and uncertainty index functions are defined and employed to devise a novel comparison method for CRETFNs. A detailed procedure is put forward to solve group decision making problems with TFARPRs. Six numerical examples are provided to illustrate the validity and applicability of the proposed models.
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影响因子：
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作者：
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影响因子：
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DOI：
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期刊：
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DOI：
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期刊：
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影响因子：
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作者：
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通讯作者：
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DOI：
10.1049/pbpo161e_ch3
发表时间：
2021-07
期刊：
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