引用本文:毛军军,张丽平.犹豫不确定离散语言Z-numbers及其基于离散T模的多准则群决策问题的应用[J].控制与决策,2020,35(2):417-426
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犹豫不确定离散语言Z-numbers及其基于离散T模的多准则群决策问题的应用
毛军军1,2, 张丽平1
(1. 安徽大学数学科学学院,合肥230601;2. 安徽大学计算智能与信号处理教育部重点实验室,合肥230601)
摘要:
介绍基于Z-numbers和语言模型的犹豫不确定离散语言Z-numbers(HUDLZNs).HUDLZNs能够有效地描述决策信息的复杂性和不确定性,并能较好地反映出决策者的犹豫性.在此基础上,提出一种基于离散T模融合和正理想方案的多准则群决策方法.首先,借助语言尺度函数来处理语言信息,并定义HUDLZNs间的距离、$\lambda$ 截集和$Cλ截集;其次,提出基于HUDLZNs的离散T模融合;再次,结合离散T模融合和语言尺度函数的优点提出一种HUDLZNs的多准则群决策方法;最后,用ERP系统选型的实例进行阐明,并通过灵敏度分析和已有方法的比较进一步表明所提出方法的有效性和可行性.
关键词:  多准则群决策  犹豫不确定离散语言Z-number  语言尺度函数  离散T模融合
DOI:10.13195/j.kzyjc.2018.0719
分类号:C934
基金项目:国家自然科学基金项目(61806001);安徽省自然科学基金项目(1708085MF163);安徽大学研究生创新训练项目(2018AHU).
Hesitant uncertain discrete linguistic Z-numbers and their application in multi-criteria group decision-making problems based on discrete T-norm
MAO Jun-jun1,2,ZHANG Li-ping1
(1. School of Mathematical Science,Anhui University,Hefei230601,China;2. Key Laboratory of Intelligent Computing and Signal Processing,Anhui University,Hefei230601,China)
Abstract:
This paper introduces hesitant uncertain discrete linguistic Z-numbers (HUDLZNs) based on Z-numbers and linguistic models. HUDLZNs can serve as a effective tool to depict complex and uncertain decision-making information and reflect the hesitancy of DMs. Based on above, a multi-criteria group decision-making(MCGDM) approach using discrete T-norm fusion and positive ideal of alternative is proposed. Firstly, linguistic information is handled with the help of the linguistic scale function, after which the distance and $\lambda$-cut of HULZNs and $\lambda$-cut of C are defined. Then, information fusion of discrete T-norm based on HUDLZNs is proposed. Subsequently, combining the very best of information fusion of discrete T-norm and linguistic scale functions, a MCGDM approach based on HUDLZNs is developed. Finally, an illustrative example of ERP system selection is provided for demonstration, and the feasibility and effectiveness of the proposed method are further proved by sensitivity analysis and comparison with an existing method.
Key words:  multi-criteria group decision-making  hesitant uncertain discrete linguistic Z-numbers  linguistic scale function  discrete T-norm fusion

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