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,李应,倪志伟,朱旭辉,伍章俊

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

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

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
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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
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摘要

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.

Abstract

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.

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.

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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. 系统科学与数学, 2020, 40(6): 1074-1080. https://doi.org/10.12341/jssms13911
WU Wenying , LI Ying , NI Zhiwei , ZHU Xuhui , WU Zhangjun. Probabilistic Hesitant Fuzzy Maclaurin Geometric Symmetric Mean Operator and Its Group Decision Making Model. Journal of Systems Science and Mathematical Sciences, 2020, 40(6): 1074-1080 https://doi.org/10.12341/jssms13911
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