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Additive Consistency-Based Decision-Making with Incomplete Probabilistic Linguistic Preference Relations
International Journal of Fuzzy Systems ( IF 4.3 ) Pub Date : 2021-07-25 , DOI: 10.1007/s40815-021-01144-4
Zi-yu Chen 1 , Fei Xiao 1 , Min-hui Deng 1, 2 , Jian-qiang Wang 1 , He-wei Liu 2
Affiliation  

Probabilistic linguistic term set (PLTS), an efficient tool to describe decision information, can sufficiently express decision makers’ hesitation and preference. Probabilistic linguistic preference relation (PLPR) is based on PLTSs to describe the preference information of experts for paired alternatives. However, in practice, due to the complexity of the problem, the incompleteness of information and the lack of professional knowledge, the incomplete PLPR (InPLPR) with missing information often appears. Therefore, this paper proposes a decision-making method under InPLPR. Firstly, in order to fully consider the specific situation of missing values, missing linguistic term-InPLTS (MLT-InPLTS) is subdivided into missing single linguistic term-InPLTS (MSLT-InPLTS) and missing multiple linguistic terms-InPLTS (MMLT-InPLTS). Then, a two-stage mathematical optimization model of missing information estimation based on additive consistency, fuzzy entropy and hesitation entropy is established. Subsequently, aiming at the unacceptable consistency of complete PLPR (CPLPR) after filling in the missing values, a consistency improvement method based on the idea of gradient descent is proposed. Afterward, probabilistic linguistic weighted averaging (PLWA) operator is used to rank alternatives. Finally, medical supplier selection is taken as an example to verify the effectiveness of the proposed decision-making method, and the robustness and advantages of this method are illustrated by sensitivity analysis and comparison with other methods.



中文翻译:

具有不完全概率语言偏好关系的基于加性一致性的决策

概率语言术语集(PLTS)是一种描述决策信息的有效工具,可以充分表达决策者的犹豫和偏好。概率语言偏好关系 (PLPR) 基于 PLTS 来描述专家对成对选择的偏好信息。但在实践中,由于问题的复杂性、信息的不完备性和专业知识的缺乏,经常出现信息缺失的不完全PLPR(InPLPR)。因此,本文提出了一种InPLPR下的决策方法。首先,为了充分考虑缺失值的具体情况,将缺失语言术语-InPLTS(MLT-InPLTS)细分为缺失单个语言术语-InPLTS(MSLT-InPLTS)和缺失多个语言术语-InPLTS(MMLT-InPLTS) . 然后,建立了基于加性一致性、模糊熵和犹豫熵的缺失信息估计两阶段数学优化模型。随后,针对填充缺失值后完全PLPR(CPLPR)一致性不可接受的问题,提出了一种基于梯度下降思想的一致性改进方法。之后,使用概率语言加权平均 (PLWA) 算子对备选方案进行排名。最后,以医疗供应商选择为例,验证了所提出的决策方法的有效性,并通过敏感性分析和与其他方法的比较说明了该方法的鲁棒性和优势。随后,针对填充缺失值后完全PLPR(CPLPR)一致性不可接受的问题,提出了一种基于梯度下降思想的一致性改进方法。之后,使用概率语言加权平均 (PLWA) 算子对备选方案进行排名。最后,以医疗供应商选择为例,验证了所提出的决策方法的有效性,并通过敏感性分析和与其他方法的比较说明了该方法的鲁棒性和优势。随后,针对填充缺失值后完全PLPR(CPLPR)一致性不可接受的问题,提出了一种基于梯度下降思想的一致性改进方法。之后,使用概率语言加权平均 (PLWA) 算子对备选方案进行排名。最后,以医疗供应商选择为例,验证了所提出的决策方法的有效性,并通过敏感性分析和与其他方法的比较说明了该方法的鲁棒性和优势。

更新日期:2021-07-25
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