| 直觉判断矩阵的弱传递性与加型一致性研究 |
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| 引用本文： | 涂振坤,张爱萍.直觉判断矩阵的弱传递性与加型一致性研究[J].浙江大学学报(理学版),2014,41(3):358-366. |
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| 作者姓名： | 涂振坤 张爱萍 |
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| 作者单位： | 合肥工业大学管理学院;合肥工业大学数学学院; |
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| 基金项目： | 国家自然科学基金资助项目(71231004,71171071);合肥工业大学校基金项目(J2014HGXJ0079) |
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| 摘 要： | 定义了直觉判断矩阵的有向图和有向路概念,证明在一定的条件下直觉判断矩阵的有向图有唯一有向路.利用该结论给出一个简洁的排序方法,并指出这种方法的不足之处.通过反例说明了直觉判断矩阵已有的加型一致性概念与弱传递性概念之间没有必然强弱关系.根据直觉模糊数的得分值和精确度值,利用效用的思想给出直觉判断矩阵加型一致性的新定义,并证明了新定义的加型一致性具有弱传递性.针对一般的直觉判断矩阵, 运用新定义的加型一致性概念以及偏差函数的方法给出了求解直觉判断矩阵的直觉模糊数型权重的模型,并通过算例验证了决策方法的实用性.
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| 关 键 词： | 直觉判断矩阵 直觉模糊数型权重 弱传递性 加型一致性 |
| 收稿时间： | 2013-04-17; |
Studying the weak transitivity property and additive consistency of intuitionistic judgment matrix |
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| TU Zhenkun,ZHANG Aiping.Studying the weak transitivity property and additive consistency of intuitionistic judgment matrix[J].Journal of Zhejiang University(Sciences Edition),2014,41(3):358-366. |
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| Authors: | TU Zhenkun ZHANG Aiping |
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| Affiliation: | 1. School of Management, Hefei University of Technology, Hefei 230009, China; 2. School of Mathematics, Hefei University of Technology, Hefei 230009, China) |
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| Abstract: | The directed graph and directed path of intuitionistic judgment matrix （IGM） are defined and it is proved that the directed graph of IGM has unique directed path under given conditions. Then a succinct ranking method is obtained and its disadvantage is pointed out . The strong and weak relation between weak transitivity and additive consistency of IGM is discussed, and it is illustrated by eounter-examples. A new definition of additive consistency of IGM is given using the idea of utility ,which is based on the values of score function and accuracy of intuitionistic fuzzy number. And it is proved that the newly defined additive consistency of IGM has weak transitivity. For general IGM, a model from which the intuitionistic fuzzy number priority weights of the IGM are obtained is given by the newly defined additive consistency of IGM and deviation function method. And the practicability of the proposed method is illustrated from an example. |
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| Keywords: | intuitionistic judgment matrix intuitionistic fuzzy number priority weight weak transitivity property additive consistency |
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