• •

### 基于TOPSIS的动态三角模糊多属性决策方法

1. 1. 福州大学经济与管理学院, 福州 350108;
2. 福建省社科研究基地福州大学福建经济高质量发展研究中心, 福州 350108;
3. 福州大学科技处, 福州 350108;
4. 莆田学院数学与金融学院, 莆田 351100
• 收稿日期:2021-06-25 修回日期:2021-10-11 出版日期:2022-04-20 发布日期:2022-04-20
• 通讯作者: 林琦,Email:Linqi1994@Yahoo.com.
• 基金资助:
国家自然科学基金项目（71872047），福建省百千万人才工程省级人选，福建省高校领军人才资助，福建省创新战略研究计划项目（2020R0021，2021R0077），福建省社科规划项目（FJ2020B024）资助课题.

LI Meijuan, YI Sicheng, QIU Qirong, LIN Qi. Dynamic Triangular Fuzzy Multi-Attribute Decision-Making Method Based on TOPSIS[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(3): 614-625.

### Dynamic Triangular Fuzzy Multi-Attribute Decision-Making Method Based on TOPSIS

LI Meijuan1,2, YI Sicheng1, QIU Qirong3, LIN Qi4

1. 1. School of Economics and Management, Fuzhou University, Fuzhou 350108;
2. Funding for Research Center of Fujian Economic High Quality Development Based on Social Science Planning of Fujian Province in China, Fuzhou 350108;
3. Department of Science and Technology, Fuzhou University, Fuzhou 350108;
4. School of Mathematics and Finance, Putian University, Putian 351100
• Received:2021-06-25 Revised:2021-10-11 Online:2022-04-20 Published:2022-04-20

For the dynamic multi-attribute decision-making problem, in which the attribute values are in the form of triangular fuzzy numbers, a dynamic triangular fuzzy multi-attribute decision-making method based on TOPSIS is proposed. Through this method, not only the degree of difference of each alternative can be obtained, but also the degree of growth of each alternative can be analyzed. At the same time, the preference parameters are set to consider the different preferences of the decision-makers for the difference and growth, and the time weight is used for secondary weighting to solve the problem of inconsistent ranking results at different time points. Finally, the necessity and importance of considering the preference of decision-makers in decision-making are illustrated by example analysis and preference parameter sensitivity analysis, and the feasibility and effectiveness of this method are further verified by comparison with other methods.

MR(2010)主题分类:

()
 [1] 张发明,华文举,李玉茹.几种综合评价方法的稳定性分析.系统科学与数学, 2019, 39(4):595-610. (Zhang F M, Hua W J, Li Y R. Stability analysis of several comprehensive evaluation methods. Journal of Systems Science and Mathematical Sciences, 2019, 39(4):595-610.)[2] 秦寿康.主成分价值函数模型及评价方案择优方法.系统科学与数学, 2001, 21(4):465-472. (Qin S K. Principal component valuation function model and method of selecting the best evaluation plan. Journal of Systems Science and Mathematical Sciences, 2001, 21(4):465-472.)[3] 宋砚秋,张玉洁,王瑶琪,等.基于多层网络的中国企业风险投资(CVC)影响力动态评价研究.系统科学与数学, 2020, 40(6):969-983. (Song Y Q, Zhang Y J, Wang Y Q, et al. Dynamic Influence evaluation based on multi-layer network of Chinese corporate venture capital (CVC). Journal of Systems Science and Mathematical Sciences, 2020, 40(6):969-983.)[4] 李美娟,李晓轩,徐林明.基于改进理想解法的动态评价方法研究.系统科学与学, 2016, 36(10):1659-1669. (Li M J, Li X X, Xu L M. Dynamic evaluation method based on improved TOPSIS. Journal of Systems Science and Mathematical Sciences, 2016, 36(10):1659-1669.)[5] 胡丽芳,关欣,邓勇,等.一种三角模糊数型多属性决策方法.控制与决策, 2011, 26(12):1877-1880. (Hu L F, Guan X, Deng Y, et al. Approach for fuzzy multi-attribute decision making. Control and Decision, 2011, 26(12):1877-1880.)[6] 林军.一类基于Hausdauff距离的模糊型多属性决策方法.系统工程学报, 2007, 22(4):367-372. (Lin J. Fuzzy multi attribute decision-making method based on Hausdauff distance. Journal of Systems Engineering, 2007, 22(4):367-372.)[7] 徐泽水. 基于FOWA算子的三角模糊数互补判断矩阵排序法.系统工程理论与实践, 2003, 23(10):86-89. (Xu Z S. A priority method for triangular fuzzy number complementary judgement matrix. Systems Engineering-Theory & Practice, 2003, 23(10):86-89.)[8] 徐泽水. 基于期望值的模糊多属性决策法及其应用.系统工程理论与实践, 2004, 24(1):109-113. (Xu Z S. Method based on expected values for fuzzy multiple attribute decision making problems with preference information on alternatives. Systems Engineering-Theory & Practice, 2004, 24(1):109-113.)[9] 杨静, 邱菀华. 基于投影技术的三角模糊数型多属性决策方法研究. 控制与决策, 2009, 24(4):637-640. (Yang J, Qiu W H. Method for multi-attribute decision-making based on projection. Control and Decision, 2009, 24(4):637-640.)[10] 张晓, 樊治平. 基于前景理论的风险型混合多属性决策方法. 系统工程学报, 2012, 27(6):772-781. (Zhang X, Fan Z P. Method for risky hybrid multiple attribute decision making based on prospect theory. Journal of Systems Engineering, 2012, 27(6):772-781.)[11] Chang Y, Yeh C, Chang Y. A new method selection approach for fuzzy group multicriteria decision making. Applied Soft Computing, 2013, 13(4):2179-2187.[12] Wang Y. The evaluation of financial performance for Taiwan container shipping companies by fuzzy TOPSIS. Applied Soft Computing, 2013, 22:28-35.[13] 陈雪, 黄智力, 罗键. 基于相对相似度关系的三角模糊数型不确定多属性决策法. 控制与决策, 2016, 31(12):2232-2240. (Chen X, Huang Z L, Luo J. Approach for triangular fuzzy number-based uncertain multi-attribute decision making based on relative similarity degree relation. Control and Decision, 2016, 31(12):2232-2240.)[14] 兰蓉, 范九伦. 三角模糊数上的完备度量及其在决策中的应用. 系统工程学报, 2010, 25(3):313-319. (Lan R, Fan J L. Complete metric on triangular fuzzy numbers and its application to decision-making. Journal of Systems Engineering, 2010, 25(3):313-319.)[15] 张市芳, 刘三阳, 秦传东, 等. 动态三角模糊多属性决策的VIKOR扩展方法. 计算机集成制造系统, 2012, 18(1):186-191. (Zhang S F, Liu S Y, Qin C D, et al. VIKOR extension method for dynamic triangular fuzzy multi-attribute decision making. Computer Intergrated Manufacturing Systems, 2012, 18(1):186-191.)[16] 张小芝, 朱传喜, 朱丽. 一种基于变权的动态多属性决策方法. 控制与决策, 2014, 29(3):494-498. (Zhang X Z, Zhu C X, Zhu L. A method of dynamic multi-attribute decision making based on variable weight. Control and Decision, 2014, 29(3):494-498.)[17] 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. 中国管理科学, 2015, 23(1):73-81. (Hao J J, Zhu J J, Liu S F. A method for multi-stage stochastic multi-criteria decision making concerning prospect theory. Chinese Journal of Management Science, 2015, 23(1):73-81.)[18] Hwang C L,Yoon K. Multiple Attribute Decision Making:Methods and Applications. New York:Springer-Verlag, 1981.[19] 陈雷,王延章.基于熵权系数与TOPSIS集成评价决策方法的研究.控制与决策, 2003, 18(4):456-459. (Chen L, Wang Y Z. Research on TOPSIS integrated evaluation and decision method based on entropy coefficient. Control and Decision, 2003, 18(4):456-459.)[20] 刘翱,童泽平,邓旭东,等.基于改进TOPSIS法的P2P网贷平台运营效率评价.系统科学与数学, 2017, 37(7):1620-1632. (Liu A, Tong Z P, Deng X D, et al. An improved TOPSIS evaluation of peer-to-peer lending's operational efficiency. Journal of Systems Science and Mathematical Sciences, 2017, 37(7):1620-1632.)[21] 华小义,谭景信.基于"垂面"距离的TOPSIS法-正交投影法.系统工程理论与实践, 2004, 24(1):114-119. (Hua X Y, Tan J X. Revised TOPSIS method based on vertical projection distance-vertical projection method. Systems Engineering-Theory & Practice, 2004, 24(1):114-119.)[22] 李美娟, 陈国宏, 林志炳, 等. 基于理想解法的动态评价方法研究. 中国管理科学, 2015, 23(10):156-161. (Li M J, Chen G H, Lin Z B, et al. Dynamic evaluation method based on TOPSIS. Chinese Journal of Management Science, 2015, 23(10):156-161.)[23] 徐林明,李美娟,欧忠辉,等.基于虚拟最劣解TOPSIS和灰关联度的动态评价方法.系统科学与数学, 2019, 39(3):365-377. (Xu L M, Li M J, Ou Z H, et al. Dynamic evaluation method based on virtual worst solution TOPSIS and gray correlation degree. Journal of Systems Science and Mathematical Sciences, 2019, 39(3):365-377.)[24] van Laarhoven P J M, Pedrycz W. A fuzzy extension of Saaty's priority theory. Fuzzy Sets and Systems, 1983, 11(1):229-241.[25] 徐泽水. 对方案有偏好的三角模糊数型多属性决策方法研究. 系统工程与电子技术, 2002, 24(8):9-12. (Xu Z S. Study on method for triangular fuzzy number based multi-attribute decision making with preference information on alternatives. Systems Engineering and Electronics, 2002, 24(8):9-12.)[26] Opricovic S. Fuzzy VIKOR with an application to water resources planning. Expert Systems with Applications, 2011, 38(10):12983-12990.[27] 张雪敏, 苏变萍, 刘美玲. 基于FOWGA算子的动态三角模糊数多属性决策法. 数学的实践与认识, 2016, 46(4):132-137. (Zhang X M, Su B P, Liu M L. A fuzzy ordered weight averaging geometric operator to multi-attribute decision making. Mathematics in Practice and Theory, 2016, 46(4):132-137.)
 [1] 李美娟, 潘瑜昕, 徐林明, 卢锦呈. 改进区间数动态 TOPSIS 评价方法[J]. 系统科学与数学, 2021, 41(7): 1891-1904. [2] 李美娟, 卢锦呈, 蔡猷花. 基于前景理论的毕达哥拉斯模糊有序加权距离TOPSIS法[J]. 系统科学与数学, 2021, 41(5): 1291-1304. [3] 李美娟, 高婧颖, 陈莞. 基于归一化双向投影法的动态评价方法[J]. 系统科学与数学, 2021, 41(10): 2730-2742. [4] 李美娟，袁宁，陈磊. 基于投影法和夹角度量法的改进TOPSIS[J]. 系统科学与数学, 2020, 40(9): 1614-1627. [5] 叶银芳，李登峰，余高锋. 需求为三角模糊数的联合订货模型及其成本分摊方法[J]. 系统科学与数学, 2019, 39(7): 1142-1158. [6] 刘翱，童泽平，邓旭东，刘克. 基于改进TOPSIS法的P2P网贷平台运营效率评价[J]. 系统科学与数学, 2017, 37(7): 1620-1632. [7] 陈振颂，李延来，CHEN Kwai-Sang. 基于二型直觉三角前景T2ITFNHA算子的多准则群决策方法[J]. 系统科学与数学, 2016, 36(8): 1226-1254. [8] 李美娟，李晓轩，徐林明. 基于改进理想解法的动态评价方法研究[J]. 系统科学与数学, 2016, 36(10): 1659-1669.