Studies on Interval Multiplicative Preference Relations and Their Application to Group Decision Making
Studies on Interval Multiplicative Preference Relations and Their Application to Group Decision Making
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DOI：
10.1007/s10726-014-9383-9
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发表时间：
2014-03
影响因子：
3
通讯作者：
M. Xia;Jian Chen
中科院分区：
文献类型：
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作者：
M. Xia;Jian Chen
研究了区间乘性偏好关系的一致性问题，并将其应用于群决策。利用可能度公式比较两个区间乘偏好值，定义了区间乘偏好关系的弱传递性。基于区间运算定义了区间乘性偏好关系的一致性，为检验区间乘性偏好关系是否一致提供了方便的手段。建立了一个目标规划模型，由区间乘性偏好关系求出区间优先权向量，该模型只需求解一个模型。通过与决策者的交互，给出了一个区间乘性偏好关系传递性的保证算法。然后将所提出的方法推广到不完全区间乘性偏好关系，该方法无需估计缺失值即可确定优先权向量。本文还提出了一种从群体乘性偏好关系中获得优先权向量的算法。该算法可以帮助决策者保证其提供的乘性偏好关系的弱传递性。
The consistency of interval multiplicative preference relations is studied and applied to group decision making. Weak transitivity for interval multiplicative preference relation is defined by comparing two interval multiplicative preferemnce values using a possibility degree formula. The consistent interval multiplicative preference relation is defined based on interval operations, which provides a convenient means to check whether an interval multiplicative preference relation is consistent. A goal-programming model is established to derive the interval priority weight vector from an interval multiplicative preference relation, which must solve only one model. An algorithm is developed through interaction with decision makers to ensure the transitivity of an interval multiplicative preference relation. The proposed methods are then extended to deal with incomplete interval multiplicative preference relations, which can determine the priority weight vector without estimating missing values. An algorithm is also developed to derive the priority vector from group multiplicative preference relations. This algorithm can help decision makers ensure the weak transitivity of their provided multiplicative preference relations.