犹豫模糊语言判断矩阵的两种加性一致性、权重导出方法及应用  

Two Additive Consistency Ascertaining, Weight Derivation and Application of Hesitant Fuzzy Linguistic Preference Relations

作　　者：许叶军 董丹迪 赖小莹 XU Yejun;DONG Dandi;LAI Xiaoying(Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190)

机构地区：[1]天津大学管理与经济学部,天津300072

出　　处：《系统科学与数学》2024年第7期1977-1994,共18页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(72271179,71871085)资助课题。

摘　　要：一致性是决策过程中关键且具有挑战性的问题之一,影响判断矩阵及决策结论的有效性和准确性.当决策者的偏好以犹豫模糊语言术语集表达时,为了有效获取语言决策环境下的决策信息,文章研究了犹豫模糊语言判断矩阵的一致性确定,不一致性修正及权重推导.首先,提出了犹豫模糊语言判断矩阵的两种加性一致性:完全加性一致性和弱加性一致性.在此基础上,提出了线性规划模型和0-1混合规划模型来确定一致性类型.另外,对于不完全的犹豫模糊语言判断矩阵,也给出了缺失值估计并判断一致性的方法;对于不一致的犹豫模糊语言判断矩阵,给出了一种修正方法,在一致性的基础上计算权重.最后,结合决策问题的具体实例并进行对比分析,验证了文章模型的有效性与合理性.Consistency is one of the key and challenging issues in decision-making processes,which affects the validity and accuracy of preference relations and decision results.When the decision makers'preference is expressed by the hesitant fuzzy linguistic term set,in order to obtain the decision information in the linguistic decision environment effectively,this paper studies the consistency ascertaining,inconsistency repairing and weight derivation for hesitant fuzzy linguistic preference relations.First,two new definitions of additive consistency for hesitant fuzzy linguistic preference relations are proposed:Completely additive consistency and weakly additive consistency.Based on the proposed definitions of additive consistency,some linear programming models and 0-1 mixed programming models are provided to ascertain the consistency.In addition,for the incomplete hesitant fuzzy linguistic preference relations,some methods are developed to estimate the missing values and ascertain the consistency.When the hesitant fuzzy linguistic preference relations are inconsistent,a repairing method is developed,then the priority weights are calculated based on the consistency.Finally,some specific examples of decision problems and comparative analysis are provided to show the effectiveness and rationality of the models.

关 键 词：犹豫模糊语言判断矩阵 加性一致性 不一致改进 权重 

分 类 号：O225[理学—运筹学与控制论] O159[理学—数学]