概率犹豫模糊Maclaurin几何对称平均算子及其群决策模型

doi:10.12341/jssms13911

系统科学与数学 ›› 2020, Vol. 40 ›› Issue (6): 1074-1080.DOI: 10.12341/jssms13911

概率犹豫模糊Maclaurin几何对称平均算子及其群决策模型

武文顺^1,2，李应^1,2，倪志伟^1,2，朱旭辉^1,2，伍章俊^1,2

1.合肥工业大学管理学院,合肥 230009;2.过程优化与智能决策教育部重点实验室,合肥 230009

出版日期:2020-06-25 发布日期:2020-08-25

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武文顺，李应，倪志伟，朱旭辉，伍章俊. 概率犹豫模糊Maclaurin几何对称平均算子及其群决策模型[J]. 系统科学与数学, 2020, 40(6): 1074-1080.

WU Wenying,LI Ying, NI Zhiwei, ZHU Xuhui,WU Zhangjun. Probabilistic Hesitant Fuzzy Maclaurin Geometric Symmetric Mean Operator and Its Group Decision Making Model[J]. Journal of Systems Science and Mathematical Sciences, 2020, 40(6): 1074-1080.

Probabilistic Hesitant Fuzzy Maclaurin Geometric Symmetric Mean Operator and Its Group Decision Making Model

WU Wenying^1,2 ,LI Ying^1,2 ,NI Zhiwei^1,2 ,ZHU Xuhui^1,2 ,WU Zhangjun^1,2

1. School of Management, Hefei University of Technology, Hefei 230009; 2. Key Laboratory of Process Optimization and Intelligent Decision-Making, Ministry of Education, Hefei 230009

Online:2020-06-25 Published:2020-08-25

属性信息的集成已经成为模糊决策领域一个重要的研究课题.基于概率犹豫模糊加权Maclaurin 几何对称平均算子构建了一种新的多属性群决策算法.首先,定义了Maclaurin 几何对称平均(MGSM) 算子,并进一步将该算子引入到概率犹豫模糊环境下, 结合Archimedean范数的思想,提出了概率犹豫模糊Maclaurin 几何对称平均(PHFMGSM)算子;其次,探讨了PHFMGSM 算子具有的优良性质以及几种特殊表达形式;随后,基于提出的概率犹豫模糊加权Maclaurin几何对称平均(PHFWMGSM)算子,构建了一种新的概率犹豫模糊多属性群决策算法;最后,通过采购数据库的实例发现, PHFWMGSM 算子性质优良、计算简单、稳定性好且灵活可靠,且提出的群决策模型是更为合理有效.

关键词： 多属性群决策, 概率犹豫模糊集, Archimedean范数, Maclaurin几何对称平均算子, 数据库选择.

Aggregation approach of attribute information is a significant research topic in fuzzy decision-making field. In this paper, a new multi-attribute group decision algorithm is constructed based on probabilistic hesitant fuzzy weighted Maclaurin geometric mean operator. Firstly, the Maclaurin geometric symmetric averaging (MGSM) operator is introduced. Under the probabilistic hesitant fuzzy environment, combing with Archimedean norm and the MGSM operator, the probabilistic hesitant fuzzy Maclaurin geometric symmetric mean (PHFMGSM) operator is proposed. Then, the excellent properties and several special forms of the PHFMGSM operator are discussed. Furthermore, a novel model of probabilistic hesitant fuzzy multi-attribute group decision making is investigated on the basis of the proposed probabilistic hesitant fuzzy weighted Maclaurin geometric symmetric mean (PHFWMGSM) operator. Finally, an example of purchasing database is provided to verify that the PHFWMGSM operator is of excellent properties, simple calculations and high stability and flexibility. In addition, the group decision model is a more reasonable and effective method.

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