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中国管理科学

中国管理科学 >

2017 , Vol. 25 >Issue 4: 174 - 183

DOI: https://doi.org/10.16381/j.cnki.issn1003-207x.2017.04.021

论文

(语言)Heronian平均算子及其决策应用

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  • 郑州航空工业管理学院理学院, 河南 郑州 450015

收稿日期: 2015-06-16

  修回日期: 2016-02-02

  网络出版日期: 2017-06-29

基金资助

国家自然科学基金资助项目（11501525）；郑州航空工业管理学院青年科研基金（2016113001）

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(Linguistic) Heronian Mean Operators and Applications in Decision Making

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  • School of Science, Zhengzhou University of Aeronautics, Zhengzhou 450015, China

Received date: 2015-06-16

  Revised date: 2016-02-02

  Online published: 2017-06-29

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摘要

多属性决策中的许多集成算子假设属性相互独立，从而导致信息集成和决策结果出现不合理的情况。Heronian平均算子是一种体现属性间相互作用的集成算子，因此研究和推广Heronian平均算子具有重要的理论和现实意义。首先，针对相关文献中的加权Heronian平均算子不具有还原性，定义了一种具有还原性的广义加权Heronian平均算子（GWHM），随后定义了三参量Heronian平均算子（TPHM）和三参量加权Heronian平均算子（TPWHM），并分别研究了它们的幂等性、单调性和有界性等性质。然后，将GWHM算子、TPHM算子和TPWHM算子分别推广到语言决策中，给出了语言加权Heronian平均算子（LWHM）以及三参量语言Heronian平均算子（TPLHM）和三参量语言加权Heronian平均算子（TPLWHM），并对它们的性质进行了探讨。最后，给出了利用（语言）Heronian平均算子进行决策的方法，并通过两个实例说明了方法的可行性。

关键词： 集成算子; Heronian平均算子; 语言Heronian平均算子; 决策

本文引用格式

刘卫锋, 常娟, 杜迎雪 . (语言)Heronian平均算子及其决策应用[J]. 中国管理科学, 2017 , 25(4) : 174 -183 . DOI: 10.16381/j.cnki.issn1003-207x.2017.04.021

Abstract

In information aggregation of multiple attribute decision making, some aggregation operators are defined based on the hypothesis in which all the attributes are mutually indenpent, resulting in unreasonable information aggregation and decision result. Heronian mean operator is an aggregation opeator in which can deal with the situation of interrelationshiop between attributes, and from the theoretical and and practical points of view, it is worth to study and generalize Heronian mean operator. Firstly, aiming at weighted Heronian mean operator without reducibility in related reference, the generalized weighted Heronian mean operator(GWHM) with reducibility is introduced. And then, the three parameters Heronian mean operator(TPHM) and the three parameters weighted Heronian mean operator(TPWHM) are defined, and their basic properties such as idempotency, monotonicity and boundness are studied. Further, in order to fulfill applications of Heronian mean operator in linguistic multiple attribute decision making, linguistic weighted Heronian mean operator(LWHM), three parameters linguisitic Heronian mean operator(TPLWHM) and three parameters linguisitic weighted Heronian mean operator(TPLHM) are dedined, and their properties such as idempotency, monotonicity and boundness are also discussed. Finally, an approach to multiple attribute decision making based on the (linguisitic) Heronian mean operators is proposed, and two practical examples are given to illustrate our results.

Key words： aggregation operator; Heronian mean operator; linguistic Heronian mean operator; decision making

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