犹豫模糊语言Heronian平均算子在多属性决策中的应用

doi:10.12005/orms.2016.0049

运筹与管理 ›› 2016, Vol. 25 ›› Issue (2): 90-97.DOI: 10.12005/orms.2016.0049

犹豫模糊语言Heronian平均算子在多属性决策中的应用

于倩,侯福均

北京理工大学管理与经济学院,北京 100081

收稿日期:2015-01-22 出版日期:2016-04-25
作者简介:于倩(1984-),女,博士研究生,研究方向:多属性决策,最优化分析;侯福均(1967-),男,副教授,博士生导师,研究方向:决策理论与方法,运筹与优化,不确定理论及应用。
基金资助:
国家自然科学基金资助项目(71571019)

Hesitant Fuzzy Linguistic Heronian Mean Operators and Their Application to Multiple Attribute Decision Making

YU Qian, HOU Fu-jun

School of Management and Economics, Beijing Institute of Technology, Beijing, 100081, China

Received:2015-01-22 Online:2016-04-25

摘要/Abstract

摘要： 针对输入变量之间的相互影响以及评价值为犹豫模糊语言信息的多属性决策问题,提出一种基于犹豫模糊语言Heronian平均算子的多属性决策方法。由于Heronian平均(HM)算子具有能够反映输入变量之间相互关联的良好特性,在犹豫模糊语言信息环境下,提出了两种新的集成算子,即犹豫模糊语言Heronian平均(HFLHM)算子和犹豫模糊语言几何Heronian平均(HFLGHM)算子,同时研究了它们的一些特性。考虑到输入变量具有不同的重要程度,还定义了犹豫模糊语言加权Heronian平均(HFLWHM)算子和犹豫模糊语言加权几何Heronian平均(HFLWGHM)算子。最后提出了基于HFLWHM算子和HFLWGHM算子的犹豫模糊语言多属性决策方法,并通过实例验证了这些算子的合理性和可行性。

关键词: 多属性决策(MADM), 犹豫模糊语言集(HFLS), 犹豫模糊语言Heronian平均 (HFLHM) 算子, 犹豫模糊语言几何Heronian平均 (HFLGHM) 算子

Abstract: For solving multiple attribute decision making(MADM)problems when the evaluation values are in the form of hesitant fuzzy linguistic sets(HFLS)and the input arguments are associated with each other, an approach based on the Heronian mean(HM)operator is proposed to aggregate the hesitant fuzzy linguistic information. Due to the desirable properties of Heronian mean(HM)operator and geometric Heronian mean(GHM)operator that they can capture the interrelationship between input arguments, a hesitant fuzzy linguistic Heronian mean(HFLHM)operator and a hesitant fuzzy linguistic geometric Heronian mean(HFLGHM)operator are proposed. Furthermore, some desirable properties and special cases of these operators are studied in detail. Considering the input arguments with different importance, the hesitant fuzzy linguistic weighted Heronian mean(HFLWHM)operator and the hesitant fuzzy linguistic weighted geometric Heronian mean(HFLWGHM)operator are defined. Moreover, based on these proposed aggregation operators, we develop an approach to deal with multiple attribute decision making problems under hesitant fuzzy linguistic environment. Finally, a numerical example is provided to illustrate the practicality and validity of the proposed method.

Key words: Multiple attribute decision making(MADM), Hesitant fuzzy linguistic sets(HFLS), hesitant fuzzy linguistic Heronian mean(HFLHM)operator, hesitant fuzzy linguistic geometric Heronian mean(HFLGHM)operator

中图分类号:

C934

于倩,侯福均. 犹豫模糊语言Heronian平均算子在多属性决策中的应用[J]. 运筹与管理, 2016, 25(2): 90-97.

YU Qian, HOU Fu-jun. Hesitant Fuzzy Linguistic Heronian Mean Operators and Their Application to Multiple Attribute Decision Making[J]. Operations Research and Management Science, 2016, 25(2): 90-97.

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犹豫模糊语言Heronian平均算子在多属性决策中的应用

Hesitant Fuzzy Linguistic Heronian Mean Operators and Their Application to Multiple Attribute Decision Making

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