Interval multiplicative transitivity for consistency, missing values and priority weights of interval fuzzy preference relations
Interval multiplicative transitivity for consistency, missing values and priority weights of interval fuzzy preference relations
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DOI：
10.1016/j.ins.2010.08.019
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发表时间：
2010-12
期刊：
影响因子：
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通讯作者：
S. Genç;F. E. Boran;D. Akay;Zeshui Xu
中科院分区：
文献类型：
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作者：
S. Genç;F. E. Boran;D. Akay;Zeshui Xu
本文给出了Tanino [T. Tanino，Fuzzy preference ordering in group decision-making，Fuzzy Sets and Systems 12（1984）117-131]，将其推广到区间模糊偏好关系是否相容，并导出相容区间模糊偏好关系的优先向量。本文通过引入区间模糊偏好关系的区间乘传递性概念来实现这一点，并通过数值算例表明，基于区间乘传递性的简单公式所得到的一致性检验和权值与Xu和Chen [Z.S. Xu，J. Chen，Some models for deriving the priority weights from interval fuzzy preference relations，European Journal of Operational Research 184（2008）266-280].此外，利用区间模糊偏好关系的区间乘传递性，提出了不完全区间模糊偏好关系缺失值的两种估计方法，并给出了数值例子.
In this paper, the concept of multiplicative transitivity of a fuzzy preference relation, as defined by Tanino [T. Tanino, Fuzzy preference orderings in group decision-making, Fuzzy Sets and Systems 12 (1984) 117–131], is extended to discover whether an interval fuzzy preference relation is consistent or not, and to derive the priority vector of a consistent interval fuzzy preference relation. We achieve this by introducing the concept of interval multiplicative transitivity of an interval fuzzy preference relation and show that, by solving numerical examples, the test of consistency and the weights derived by the simple formulas based on the interval multiplicative transitivity produce the same results as those of linear programming models proposed by Xu and Chen [Z.S. Xu, J. Chen, Some models for deriving the priority weights from interval fuzzy preference relations, European Journal of Operational Research 184 (2008) 266–280]. In addition, by taking advantage of interval multiplicative transitivity of an interval fuzzy preference relation, we put forward two approaches to estimate missing value(s) of an incomplete interval fuzzy preference relation, and present numerical examples to illustrate these two approaches.