基于q阶orthopair模糊集和参考理想法的多准则决策方法

doi:10.16381/j.cnki.issn1003-207x.2020.1456

中国管理科学 ›› 2023, Vol. 31 ›› Issue (10): 245-253.doi: 10.16381/j.cnki.issn1003-207x.2020.1456

• • 上一篇

基于q阶orthopair模糊集和参考理想法的多准则决策方法

王浩伦^1,²,张发明³(),完颜晓盼²,韩雪⁴

^1.南昌航空大学经济管理学院, 江西南昌 330063
^2.南昌大学经济管理学院, 江西南昌 330031
^3.桂林电子科技大学商学院, 广西桂林 541004
^4.华东交通大学交通运输与物流学院, 江西南昌 330013

收稿日期:2020-07-29 修回日期:2021-01-20 出版日期:2023-10-15 发布日期:2023-11-03
通讯作者: 张发明 E-mail:zfm1214@163.com
基金资助:
国家自然科学基金资助项目(72361026);教育部人文社会科学基金资助项目(21XJA630009);广西自然科学基金资助项目(2021JJA180078);广西哲学社会科学规划项目(21FGL037);江西省主要学科学术和技术带头人项目(20194BCJ22001);江西省博士后科研资助项目(2019KY14)

A Multi-Criteria Decision-Making Method Based on q-Rung Orthopair Fuzzy Set and Reference Ideal Method

Hao-lun WANG^1,²,Fa-ming ZHANG³(),WAN-YAN Xiao-pan²,Xue HAN⁴

^1.School of Economics and Management, Nanchang Hangkong University, Nanchang 330063, China
^2.School of Economics and Management, Nanchang University, Nanchang 330031, China
^3.School of Business, Guilin University of Electronic Technology, Guilin 541004, China
^4.School of Transportation and Logistics, East China JiaoTong University, Nanchang 330013, China

Received:2020-07-29 Revised:2021-01-20 Online:2023-10-15 Published:2023-11-03
Contact: Fa-ming ZHANG E-mail:zfm1214@163.com

摘要/Abstract

摘要：

针对现有决策方法理想解确定不合理和秩反转的问题，提出一种基于q阶orthopair模糊集（q-rung orthopair fuzzy set， q-ROFS）和参考理想法（reference ideal method， RIM）的多准则决策方法。在q-ROFS概念基础上分别定义了q-ROF可能度和q-ROFS交叉熵，并讨论其相关性质；将传统RIM在q-ROF环境下进行扩展，构建一种基于q-ROFRIM的多准则决策模型，利用q-ROF可能度确定准则最优权重以及作为q-ROF信息差异程度测度的q-ROF交叉熵替代传统RIM中距离测度。最后通过实例分析说明该方法可行和有效，方法对比结果表明，所提方法不仅使决策过程更加科学和合理，而且能够解决秩反转问题。

关键词: q-ROFS, q-ROF可能度, q-ROFS交叉熵, q-ROFRIM, 多准则决策

Abstract:

Among traditional decision methods， such as TOPSIS and VIKOR， the maximum or minimum value is considered to be the best choice， but the best choice may occur between the maximum and minimum value in the real world， such as the temperature suitable for plant growth. Meanwhile， q-rung orthopair fuzzy set （q-ROFS） can help decision-makers express their opinions freely and comprehensively in the face of complex decision-making problems.To solve the problems of unreasonable determination of ideal solution and rank reversal in existing decision-making methods， a multi-criteria decision-making method based on q-ROFS and reference ideal method （RIM） is proposed. Firstly， the q-rung orthopair fuzzy （q-ROF） possibility degree and q-ROFS cross entropy are defined respectively， and their related properties are discussed； Secondly， the traditional RIM is extended in the q-ROF environment， and a multi-criteria decision-making model based on q-ROFRIM is built， where the q-ROF possibility degree is used to determine the optimal weight of the criteria， and the q-ROF cross entropy， as a measure of the information difference degree of q-ROF， is used to replace the distance measure in the traditional RIM. Finally， an example analysis illustrates the feasibility and effectiveness of the proposed method. In addition， comparison with previous methods shows that the proposed method not only makes the decision process more scientific and reasonable， but also avoids the rank reversal problem.

Key words: q-rung orthopair fuzzy set, q-ROF possibility, q-ROFS cross entropy, q-ROFRIM, multi-criteria decision making

中图分类号:

C934

王浩伦,张发明,完颜晓盼,韩雪. 基于q阶orthopair模糊集和参考理想法的多准则决策方法[J]. 中国管理科学, 2023, 31(10): 245-253.

Hao-lun WANG,Fa-ming ZHANG,WAN-YAN Xiao-pan,Xue HAN. A Multi-Criteria Decision-Making Method Based on q-Rung Orthopair Fuzzy Set and Reference Ideal Method[J]. Chinese Journal of Management Science, 2023, 31(10): 245-253.

图/表 5

图1

表1

准则的取值范围和理想参考范围"

准则	$R ? j$	$I ? j$
C₁	[<0.20,0.98>,<0.98,0.20>]	[<0.87,0.35>,<0.98,0.20>]
C₂	[<0.20,0.98>,<0.98,0.20>]	[<0.87,0.35>,<0.98,0.20>]
C₃	[<0.20,0.98>,<0.98,0.20>]	[<0.70,0.40>,<0.98,0.20>]
C₄	[<0.20,0.98>,<0.98,0.20>]	[<0.87,0.25>,<0.98,0.20>]

表1

表2

表3

方法对比分析结果"

方法	A₁	A₂	A₃	A₄	排序
q-ROFWA	sc(A₁)=0.567	sc(A₂)=0.701	sc(A₃)=0.665	sc(A₄)=0.703	$A 4 > A 2 > A 3 > A 1$
q-ROFWG	sc(A₁)=0.512	sc(A₂)=0.656	sc(A₃)=0.645	sc(A₄)=0.647	$A 2 > A 4 > A 3 > A 1$
q-ROFTOPSIS	CI(A₁)=0.102	CI(A₂)=0.555	CI(A₃)=0.476	CI(A₄)=0.598	$A 4 > A 2 > A 3 > A 1$
q-ROFVIKOR	Q(A₁)=1.000	Q(A₂)=0.000	Q(A₃)=0.486	Q(A₄)=0.436	$A 2 > A 4 > A 3 > A 1$
本文方法	RI₁=0.806	RI₂=0.938	RI₃=0.873	RI₄=0.909	$A 2 > A 4 > A 3 > A 1$

表3

表4

关于秩反转问题的各方法对比"

方法	A₁	A₂	A₃	A₄	A₅	排序
q-ROFWA	sc(A₁)=0.580	sc(A₂)=0.690	sc(A₃)=0.684	sc(A₄)=0.686	sc(A₅)=0.657	$A 2 > A 4 > A 3 > A 5 > A 1$
q-ROFWG	sc(A₁)=0.533	sc(A₂)=0.637	sc(A₃)=0.659	sc(A₄)=0.627	sc(A₅)=609	$A 3 > A 2 > A 4 > A 5 > A 1$
q-ROFTOPSIS	CI(A₁)=0.195	CI(A₂)=0.548	CI(A₃)=0.558	CI(A₄)=0.599	CI(A₅)=0.467	$A 4 > A 3 > A 2 > A 5 > A 1$
本文方法	RI₁=0.802	RI₂=0.934	RI₃=0.871	RI₄=0.911	RI₅=0.810	$A 2 > A 4 > A 3 > A 5 > A 1$

表4

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方案	I_i⁺	I_i^-	RI_i	排序
A₁	0.103	0.430	0.806	4
A₂	0.032	0.479	0.938	1
A₃	0.064	0.439	0.873	3
A₄	0.047	0.469	0.909	2

[1]	郝晶晶, 朱建军, 刘思峰. 基于前景理论的多阶段随机多准则决策方法[J]. 中国管理科学, 2015, 23(1): 73-81.
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[3]	李春好, 陈煦, 梁琼, 孙永河. DEA决策单元的广义价值效率测度模型[J]. 中国管理科学, 2005, (6): 91-96.

基于q阶orthopair模糊集和参考理想法的多准则决策方法

A Multi-Criteria Decision-Making Method Based on q-Rung Orthopair Fuzzy Set and Reference Ideal Method

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