分布式乘性偏好环境下考虑决策者偏好调整意愿的最优-最劣多准则决策方法

doi:10.16381/j.cnki.issn1003-207x.2021.1586

中国管理科学 ›› 2024, Vol. 32 ›› Issue (7): 65-75.doi: 10.16381/j.cnki.issn1003-207x.2021.1586cstr: 32146.14.j.cnki.issn1003-207x.2021.1586

分布式乘性偏好环境下考虑决策者偏好调整意愿的最优-最劣多准则决策方法

杨荣庆^1,^2,³,唐孝安^1,^2,³(),张强^1,^2,³,黄挺^1,^2,³

^1.合肥工业大学管理学院, 安徽合肥 230009
^2.过程优化与智能决策教育部重点实验室, 安徽合肥 230009
^3.智能决策与信息系统技术教育部工程研究中心, 安徽合肥 230009

收稿日期:2021-08-11 修回日期:2021-12-08 出版日期:2024-07-25 发布日期:2024-08-07
通讯作者: 唐孝安 E-mail:tangxa@hfut.edu.cn
基金资助:
国家自然科学基金项目(72101075);安徽省自然科学基金项目(2108085QG289);中央高校基本科研业务费专项(JZ2022HGTB0286)

Best-worst Multi-criteria Decision-making Method with Decision Maker's Preference Adjustment Willingness under Distributed Multiplicative Preference Environment

Rongqing Yang^1,^2,³,Xiaoan Tang^1,^2,³(),Qiang Zhang^1,^2,³,Ting Huang^1,^2,³

^1.School of Management，Hefei University of Technology，Hefei 230009，China
^2.Key Laboratory of Process Optimization and Intelligent Decision-Making，Ministry of Education，Hefei 230009，China
^3.Engineering Research Center of Intelligent Decision-Making and Information System Technology，Ministry of Education，Hefei 230009，China

Received:2021-08-11 Revised:2021-12-08 Online:2024-07-25 Published:2024-08-07
Contact: Xiaoan Tang E-mail:tangxa@hfut.edu.cn

摘要/Abstract

摘要：

本文研究了分布式乘性偏好环境下的多准则决策问题。一方面，为了处理乘性偏好多准则决策问题中决策者采用语言等级刻画准则之间偏好强度时，在语言等级的选择上可能存在的犹豫不确定性，以及在采用多个语言等级但对每个语言等级有明确偏好度的问题，首次提出了分布式乘性偏好关系的概念。该偏好关系在刻画决策者关于准则之间的偏好强度时既继承了乘性偏好值的有效性，又解决了决策者在多个可能乘性偏好值之间选择时存在的犹豫问题。另一方面，针对传统Best-Worst Method（BWM）对不满足一致性要求的偏好进行迭代调整时，未考虑决策者自身调整意愿和调整过程复杂、计算工作量大等局限问题，在分布式乘性偏好环境下构建了考虑决策者偏好调整意愿的BWM。该改进的BWM在最大化保留决策者原始偏好的同时，能使偏好快速达到一致性要求。关于某公司商业用车的决策案例验证了本文方法在应用方面的可行性和有效性。

关键词: 多准则决策, BWM, 分布式乘性偏好关系, 一致性, 偏好调整意愿

Abstract:

Comparison matrices show sound performance when representing the outcomes of pairwise comparisons coming from decision-makers. Over the past decades， numerous researchers have investigated multi-criteria decision-making with different forms of comparison matrices， including multiplicative preference relations， interval multiplicative preference relations and hesitant multiplicative preference relations. But one can also note there are situations where the outlined comparison matrices fail to record decision-makers’ preference information. To address the limitations of the aforesaid preference relations， this study focusses on the multi-criteria decision-making problem under distributed multiplicative preference environment. First， a new way of pairwise comparison called distributed multiplicative preference relations is introduced to address the hesitation on the linguistic term selection of decision makers when they use linguistic variables to depict their preference information of one criterion over another， and the case where decision makers show tendencies to provide some specific degrees on certain linguistic terms in multiplicative preference multi-criteria decision-making. This newly-introduced preference relation not only inherits the superiority of multiplicative preference but also can handle the hesitation of decision makers on the problem of linguistic term selection when being used to express the preferences over criteria. Then， an improved Best-Worst Method （BWM） with distributed multiplicative preferences is proposed by considering decision maker’s preference adjustment willingness to overcome such limitations as the neglect of decision maker’s willingness， the high computational burden， and the complicated consistency adjustment process of the traditional BWM in managing inconsistent multiplicative preferences. The improved BWM can achieve a predetermined consistency level efficiently in the setting of retaining the original preferences of decision makers to the greatest extent. Finally， a commercial vehicle purchase decision problem is analyzed by using the proposals to demonstrate their feasibility and validity in practice.

Key words: multi-criteria decision-making, Best-worst method, distributed multiplicative preference relation, consistency, preference adjustment willingness

中图分类号:

C934

杨荣庆,唐孝安,张强,黄挺. 分布式乘性偏好环境下考虑决策者偏好调整意愿的最优-最劣多准则决策方法[J]. 中国管理科学, 2024, 32(7): 65-75.

Rongqing Yang,Xiaoan Tang,Qiang Zhang,Ting Huang. Best-worst Multi-criteria Decision-making Method with Decision Maker's Preference Adjustment Willingness under Distributed Multiplicative Preference Environment[J]. Chinese Journal of Management Science, 2024, 32(7): 65-75.

图/表 10

图1

表1

表2

表3

表4

表5

表6

表7

表8

表9

参考文献 33

1	Wang Y M， Yang J B， Xu D L. A two-stage logarithmic goal programming method for generating weights from interval comparison matrices［J］. Fuzzy Sets and Systems， 2005， 152（3）： 475-498.
2	Liu M， Zhou W， Duan Y L. Generalized hesitant multiplicative preference relations and the analytic risk-network process［J］. Information Sciences， 2020， 540： 345-369.
3	Liu W Q， Zhang H J， Chen X， et al. Managing consensus and self-confidence in multiplicative preference relations in group decision making［J］. Knowledge-Based Systems， 2018， 162： 62-73.
4	Calvo T， Fuster P， Martín J， et al. Aggregation for linearly ordered fuzzy preference relations based on consistency［J］. Fuzzy Sets and Systems， 2022，446：38-52.
5	Wang Z J， Yang X， Jin X T. And-like-uninorm-based transitivity and analytic hierarchy process with interval-valued fuzzy preference relations［J］. Information Sciences， 2020， 539： 375-396.
6	Zhang Q， Huang T， Tang X A， et al. A linguistic information granulation model and its penalty function-based co-evolutionary PSO solution approach for supporting GDM with distributed linguistic preference relations［J］. Information Fusion， 2021， 77： 118-132.
7	Liu H B， Jiang L. Optimizing consistency and consensus improvement process for hesitant fuzzy linguistic preference relations and the application in group decision making［J］. Information Fusion， 2020， 56： 114-127.
8	Tang X A， Peng Z L， Zhang Q， et al. Consistency and consensus-driven models to personalize individual semantics of linguistic terms for supporting group decision making with distribution linguistic preference relations［J］. Knowledge-Based Systems， 2020， 189： 105078.
9	Saaty T. The analytical hierarchy process［M］. New York： McGraw-Hill Press， 1980.
10	Girsang A S， Tsai C W， Yang C S. Ant algorithm for modifying an inconsistent pairwise weighting matrix in an analytic hierarchy process［J］. Neural Computing and Application， 2015， 26： 313-327.
11	Wu Z B， Xu J P. A consistency and consensus-based decision support model for group decision making with multiplicative preference relations［J］. Decision Support Systems， 2012， 52（3）： 757-767.
12	Saaty T L， Vargas L G. Uncertainty and rank order in the analytic hierarchy process［J］. European Journal of Operational Research， 1987， 32： 107-117.
13	Xia M M， Xu Z S. Managing hesitant information in GDM problems under fuzzy and multiplicative preference relations［J］. International Journal of Uncertainty， Fuzziness and Knowledge-Based Systems， 2013， 21（6）： 865-897.
14	Wang Y M， Elhag T. A goal programming method for obtaining interval weights from an interval comparison matrix［J］. European Journal of Operational Research， 2007， 177（1）： 458-471.
15	Cheng X J， Wan S P， Dong J Y. A new consistency definition of interval multiplicative preference relation［J］. Fuzzy Sets and Systems， 2020， 409： 55-84.
16	Zhang Z M， Wu C. A decision support model for group decision making with hesitant multiplicative preference relations［J］. Information Sciences， 2014， 282： 136-166.
17	Wang Y M， Fan Z P， Hua Z S. A chi-square method for obtaining a priority vector from multiplicative and fuzzy preference relations［J］. European Journal of Operational Research， 2007， 182（1）： 356-366.
18	Coffey L， Claudio D. In defense of group fuzzy AHP： A comparison of group fuzzy AHP and group AHP with confidence intervals［J］. Expert Systems with Applications， 2021， 178： 114970.
19	Dhanaraj P S， Rathinasuriyan C. Selection of intense energy welding process for high strength aluminum alloy using AHP［J］. Materials Today： Proceedings， 2021， 46： 8254-8259.
20	Rezaei J. Best-worst multi-criteria decision-making method［J］. Omega， 2015， 53： 49-57.
21	Omrani H， Alizadeh A， Amini M. A new approach based on BWM and Multimoora methods for calculating semi-human development index： An application for provinces of Iran［J］. Socio-Economic Planning Sciences， 2020， 70： 100689.
22	Gupta H， Barua M K. Identifying enablers of technological innovation for Indian MSMEs using best-worst multi criteria decision making method［J］. Technological Forecasting & Social Change， 2016， 107： 69–79.
23	Salimi N， Rezaei J. Evaluating firms’ R & D performance using best worst method［J］. Evaluation & Program Planning， 2018， 66：147-155.
24	Rezaei J， Kothadiya O， Tavasszy L， et al. Quality assessment of airline baggage handling systems using SERVQUAL and BWM［J］. Tourism Management， 2018， 66： 85-93.
25	Pamucar D， Petrovic I， Cirovic G. Modification of the best-worst and mabac methods： A novel approach based on interval-valued fuzzy-rough numbers［J］. Expert Systems with Applications， 2017， 91： 89-106.
26	Palanisamy M， Pugalendhi A， Ranganathan R. Selection of suitable additive manufacturing machine and materials through best-worst method （BWM）［J］. The International Journal of Advanced Manufacturing Technology， 2020， 107（5）： 2345-2362.
27	Tian Z P， Zhang H Y， Wang J Q， et al. Green supplier selection using improved topsis and best-worst method under intuitionistic fuzzy environment［J］. Informatica， 2018， 29（4）： 773-800.
28	Mou Q， Xu Z S， Liao H C. An intuitionistic fuzzy multiplicative best-worst method for multi-criteria group decision making［J］. Information Sciences， 2016， 374： 224-239.
29	Mi X M， Liao H C. An integrated approach to multiple criteria decision making based on the average solution and normalized weights of criteria deduced by the hesitant fuzzy best-worst method［J］. Computers & Industrial Engineering， 2019， 133： 83-94.
30	Gupta H. Assessing organizations performance on the basis of GHRM practices using BWM and fuzzy TOPSIS［J］. Journal of Environmental Management， 2018， 226： 201-216.
31	Mi X M， Tang M， Liao H C， et al. The state-of-the-art survey on integrations and applications of the best-worst method in decision making： Why， what， what for and what’s next？［J］. Omega， 2019， 87： 205-225.
32	Wan S P， Dong J Y. A novel extension of best-worst method with intuitionistic fuzzy reference comparisons［J］.IEEE Transactions on Fuzzy Systems， 2022， 30（6）： 1698-1711.
33	Yazdi M， Nedjati A， Zarei E， et al. A reliable risk analysis approach using an extension of best-worst method based on democratic-autocratic decision-making style［J］. Journal of Cleaner Production， 2020， 256： 120418.

准则	c₁	c₂	c₃	c₄	c₅	c₆
最优准则(c₁)	-	{(r⁽⁴⁾:0.1), (r⁽³⁾:0.1), (r⁽²⁾:0.3), (r⁽¹⁾:0.3)}	{(r⁽³⁾:0.2), (r⁽¹⁾:0.6)}	{(r⁽⁵⁾:0.1), (r⁽³⁾:0.6), (r⁽¹⁾:0.1)}	{(r⁽³⁾:0.3), (r⁽²⁾:0.4), (r⁽¹⁾:0.3)}	{(r⁽⁵⁾:1)}
最劣准则(c₆)	{(r⁽⁵⁾:1)}	{(r⁽³⁾:0.2), (r⁽¹⁾:0.6)}	{(r⁽⁴⁾:0.1), (r⁽³⁾:0.1), (r⁽²⁾:0.3), (r⁽¹⁾:0.3)}	{(r⁽³⁾:0.3), (r⁽¹⁾:0.7)}	{(r⁽³⁾:0.3), (r⁽²⁾:0.4), (r⁽¹⁾:0.3)}	-

准则 (c₁)	x₁	x₂	x₃	x₄	x₅
最优方案(x₂)	{(r⁽⁴⁾:0.1), (r⁽³⁾:0.2), (r⁽²⁾:0.3), (r⁽¹⁾:0.4)}	-	{(r⁽²⁾:0.4), (r⁽¹⁾:0.6)}	{(r⁽⁴⁾:0.3), (r⁽³⁾:0.7)}	{(r⁽⁵⁾:1)}
最劣方案(x₅)	{(r⁽⁴⁾:0.2), (r⁽³⁾:0.1), (r⁽¹⁾:0.7)}	{(r⁽⁵⁾:1)}	{(r⁽⁵⁾:0.1), (r⁽⁴⁾:0.5), (r⁽³⁾:0.4)}	{(r⁽⁵⁾:0.1), (r⁽³⁾:0.1), (r⁽²⁾:0.4), (r⁽¹⁾:0.4)}	-

准则 (c₂)	x₁	x₂	x₃	x₄	x₅
最优方案(x₂)	{(r⁽²⁾:0.5), (r⁽¹⁾:0.5)}	-	{(r⁽³⁾:0.1), (r⁽²⁾:0.4), (r⁽¹⁾:0.3)}	{(r⁽⁵⁾:1)}	{(r⁽⁴⁾:0.1), (r⁽³⁾:0.3), (r⁽²⁾:0.6)}
最劣方案(x₄)	{(r⁽⁵⁾:0.6)}	{(r⁽⁵⁾:1)}	{(r⁽³⁾:0.2), (r⁽²⁾:0.8)}	-	{(r⁽²⁾:0.4), (r⁽¹⁾:0.6)}

准则 (c₃)	x₁	x₂	x₃	x₄	x₅
最优方案(x₁)	-	{(r⁽⁵⁾:0.1), (r⁽³⁾:0.1), (r⁽²⁾:0.4), (r⁽¹⁾:0.4)}	{(r⁽⁵⁾:1)}	{(r⁽⁴⁾:0.1), (r⁽³⁾:0.3), (r⁽²⁾:0.6)}	{(r⁽³⁾:0.4), (r⁽²⁾:0.6)}
最劣方案(x₃)	{(r⁽⁵⁾:1)}	{(r⁽³⁾:0.4), (r⁽²⁾:0.6)}	-	{(r⁽²⁾:0.4), (r⁽¹⁾:0.6)}	{(r⁽³⁾:0.2), (r⁽²⁾:0.5), (r⁽¹⁾:0.3)}

准则 (c₄)	x₁	x₂	x₃	x₄	x₅
最优方案(x₄)	{(r⁽⁴⁾:0.1), (r⁽³⁾:0.3), (r⁽²⁾:0.6)}	{(r⁽⁵⁾:0.1), (r⁽³⁾:0.1), (r⁽²⁾:0.4), (r⁽¹⁾:0.4)}	{(r⁽⁵⁾:1)}	-	{(r⁽³⁾:0.4), (r⁽²⁾:0.6)}
最劣方案(x₃)	{(r⁽²⁾:0.4), (r⁽¹⁾:0.6)}	{(r⁽³⁾:0.4), (r⁽²⁾:0.6)}	-	{(r⁽⁴⁾:1)}	{(r⁽³⁾:0.2), (r⁽²⁾:0.5), (r⁽¹⁾:0.3)}

分布式乘性偏好环境下考虑决策者偏好调整意愿的最优-最劣多准则决策方法

Best-worst Multi-criteria Decision-making Method with Decision Maker's Preference Adjustment Willingness under Distributed Multiplicative Preference Environment

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 10

参考文献 33

相关文章 15

Metrics

本文评价

推荐阅读 0

准则 (c₅)	x₁	x₂	x₃	x₄	x₅
最优方案(x₅)	{(r⁽⁵⁾:0.1), (r⁽³⁾:0.1), (r⁽²⁾:0.4), (r⁽¹⁾:0.4)}	{(r⁽⁵⁾:1)}	{(r⁽⁴⁾:0.1), (r⁽³⁾:0.3), (r⁽²⁾:0.6)}	{(r⁽³⁾:0.4), (r⁽²⁾:0.6)}	-
最劣方案(x₂)	{(r⁽³⁾:0.4), (r⁽²⁾:0.6)}	-	{(r⁽²⁾:0.4), (r⁽¹⁾:0.6)}	{(r⁽³⁾:0.2), (r⁽²⁾:0.5), (r⁽¹⁾:0.3)}	{(r⁽⁵⁾:1)}

准则 (c₆)	x₁	x₂	x₃	x₄	x₅
最优方案(x₃)	{(r⁽⁴⁾:0.3), (r⁽³⁾:0.3), (r⁽²⁾:0.4)}	{(r⁽³⁾:0.6), (r⁽²⁾:0.4)}	-	{(r⁽³⁾:0.4), (r⁽²⁾:0.6)}	{(r⁽⁵⁾:1)}
最劣方案(x₅)	{(r⁽²⁾:0.5), (r⁽¹⁾:0.5)}	{(r⁽³⁾:0.6), (r⁽²⁾:0.4)}	{(r⁽⁵⁾:1)}	{(r⁽³⁾:0.3), (r⁽²⁾:0.5), (r⁽¹⁾:0.2)}	-

[1]	焦阳,李刚,李建平,王斌,张志鹏. 考虑专家有效信息的群决策赋权方法研究[J]. 中国管理科学, 2024, 32(8): 107-116.
[2]	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.
[3]	张鹏, 李影, 曾永泉. 现实约束下多阶段模糊投资组合的时间一致性策略研究[J]. 中国管理科学, 2022, 30(4): 42-51.
[4]	任嵘嵘, 孟一鸣, 李晓奇, 赵萌. 基于一致性度量的概率模糊语言多属性群决策方法[J]. 中国管理科学, 2020, 28(4): 220-230.
[5]	金飞飞, 倪志伟, 陈华友, 朱旭辉, 武文颖. 基于一致性局部调整算法和DEA的语言偏好决策模型[J]. 中国管理科学, 2019, 27(12): 152-163.
[6]	杨瑛哲, 黄光球. 基于企业转型目标的产品组合策略选择模型[J]. 中国管理科学, 2018, 26(7): 179-186.
[7]	苗蕊, 徐健. 评分不一致性对在线评论有用性的影响——归因理论的视角[J]. 中国管理科学, 2018, 26(5): 178-186.
[8]	李爱华, 宿洁, 贾传亮. 经济增长与碳排放协调发展及一致性模型研究——宏观低碳经济的数理分析[J]. 中国管理科学, 2017, 25(4): 1-6.
[9]	施亮, 鲁耀斌, 杨水清. 感知一致性对消费者移动购物行为的影响:基于Web-移动的跨渠道视角[J]. 中国管理科学, 2017, 25(4): 70-77.
[10]	丁涛, 吴华清, 梁樑. 360度评估体系中权重调整方法研究[J]. 中国管理科学, 2016, 24(7): 149-154.
[11]	施晓菁, 梁循, 孙晓蕾. 基于在线评级和评论的评价者效用机制研究[J]. 中国管理科学, 2016, 24(5): 149-157.
[12]	李美娟, 徐林明, 陈国宏. 基于一致性的动态组合评价方法研究[J]. 中国管理科学, 2016, 24(10): 149-155.
[13]	王洪波, 罗贺, 杨善林. 基于流形学习的非一致性判断矩阵排序方法[J]. 中国管理科学, 2015, 23(10): 147-155.
[14]	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.
[15]	刘勇, 刘思峰, Jeffrey Forrest . 一种新的灰色绝对关联度模型及其应用[J]. 中国管理科学, 2012, 20(5): 173-177.