Mathematical programming methods for consistency and consensus in group decision making with intuitionistic fuzzy preference relations
Mathematical programming methods for consistency and consensus in group decision making with intuitionistic fuzzy preference relations
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DOI：
10.1016/j.knosys.2015.12.007
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发表时间：
2016-04
期刊：
影响因子：
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通讯作者：
Gai-li Xu;S. Wan;Feng Wang;Jiu-ying Dong;Yi-feng Zeng
中科院分区：
文献类型：
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作者：
Gai-li Xu;S. Wan;Feng Wang;Jiu-ying Dong;Yi-feng Zeng
在具有直觉模糊偏好关系（IFPR）的群体决策（GDM）中，一致性和共识是两个关键问题。本文开发了一种检查和提高单个 IFPR 的一致性和专家共识的新方法。为了衡量IFPR的一致性程度，引入一致性指标，然后定义可接受的一致性。对于一致性不可接受的 IFPR，开发了数学规划方法来提高其一致性。为了评价专家之间的共识程度，用一位专家与其他专家之间的接近程度来表示共识程度。当几个单独的 IFPR 的一致性不可接受或共识不可接受时，就会建立一个目标计划来同时提高一致性和共识。根据各个IFPR的一致性和接近度，确定专家的客观权重。结合专家的主观权重，得出专家的综合权重。然后，提出了一种直观的模糊几何加权平均（IFGWM）算子，将单个 IFPR 集成为一个集体 IFPR。此外，还证明了一个有吸引力的性质：如果所有个体 IFPR 都是可接受一致的，则集体 IFPR 是可接受一致的。提供了两个例子来说明所提出方法的有效性。
In group decision making (GDM) with intuitionistic fuzzy preference relations (IFPRs), the consistency and consensus are two key issues. This paper develops a novel method for checking and improving the consistency of individual IFPRs and the consensus among experts. To measure the consistency degree of IFPRs, a consistency index is introduced and then an acceptable consistency is defined. For an IFPR with unacceptable consistency, a mathematical programming approach is developed to improve its consistency. To evaluate the consensus degree among experts, a consensus measure is presented by the proximity degree between one expert and other experts. When several individual IFPRs are unacceptable consistent or consensus is unacceptable, a goal program is built to improve the consistency and consensus simultaneously. By the consistency and proximity degrees of individual IFPRs, experts’ objective weights are determined. Combining the experts’ subjective weights, the experts’ comprehensive weights are derived. Then, an intuitionistic fuzzy geometric weighted mean (IFGWM) operator is proposed to integrate individual IFPRs into a collective one. Moreover, an attractive property is proved that the collective IFPR is acceptable consistent if all individual IFPRs are acceptable consistent. Two examples are provided to illustrate the validity of the proposed method.