Picture Fuzzy Power Geometric Heronian Mean Operators and Their Application to Multi-Criteria Decision Making

doi:10.12005/orms.2020.0314

Abstract

Abstract: In order to solve the multi-attribute decision making problem in which the attribute values are in the form of picture fuzzy number, in this paper, we combine the geometric Heronian mean operator and the power geometric operator in the classical category, and propose the picture fuzzy power geometric Heronian mean(PFPGHM) operator and picture fuzzy weighted power geometric Heronian mean operator (PFWPGHM). The proposed operator can not only reflect the correlation between the aggregated data, but also reflect the integrity of the decision process, and reduce the impact of the aggregated data with the overall information deviation on the decision result. The mathematical expressions are derived and the related properties are proposed. A multi-attribute decision making method based on PFWPGHM operator is proposed, and the influence of parameters p and q on decision making results is analyzed by practical example. Meanwhile, the feasibility and advantages of the proposed method is illustrated by comparison analysis.

Key words: picture fuzzy number, picture fuzzy power geometric Heronian mean (PFPGHM) operator, picture fuzzy weighted power geometric Heronian mean (PFWPGHM) operator, multi-criteria decision making (MCDM)

摘要： 针对决策信息为Picture模糊数的多属性决策问题,将经典范畴内的几何Heronian平均算子和幂几何算子结合,提出了Picture模糊幂几何Heronian平均(PFPGHM)算子与Picture模糊加权幂几何Heronian平均(PFWPGHM)算子。该类算子不仅能体现待集结数据间的关联性,而且还能反映决策过程中信息的整体性,降低了与整体信息偏差较大的待集结数据对决策结果的影响。推导其数学表达式,证明相关性质。提出了基于PFWPGHM算子的多属性决策方法,通过决策实例分析了参数p和q对决策结果的影响,并对比分析新方法与现存的决策方法,进而表明所研究方法的可行性与优点。

关键词: Picture模糊数, Picture模糊幂几何Heronian平均(PFPGHM)算子, Picture模糊加权幂几何Heronian平均(PFWPGHM)算子, 多属性决策(MCDM)

CLC Number:

C934

WANG Lei, TAO Liu-qin. Picture Fuzzy Power Geometric Heronian Mean Operators and Their Application to Multi-Criteria Decision Making[J]. Operations Research and Management Science, 2020, 29(12): 59-66.

王磊, 陶刘芹. Picture模糊幂几何Heronian平均算子及其在多属性决策中的应用[J]. 运筹与管理, 2020, 29(12): 59-66.

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