Recent advances in robust credibilistic optimization

doi:10.3969/j.issn.1000-1565.2021.05.002

Abstract

Abstract: Robust credibilistic optimization method is an effective modeling tool to deal with the uncertainty in fuzzy credibility distribution. This paper reviews some new developments of robust credibilistic optimization in recent years. As for the theory of robust credibilistic optimization, this paper reviews the definition of parameter selection variables under different fluctuation modes and their relationship with the construction of ambiguous distribution sets, from the distinction of vertical and horizontal fluctuation directions to the setting of single parameter and double parameter selection. On the practical research of robust credibilistic optimization, we introduce some application problems, such as inventory,- DOI:10.3969/j.issn.1000-1565.2021.05.002鲁棒可信性优化的新进展刘彦奎,刘颖(河北大学数学与信息科学学院,河北保定 071002)刘彦奎教授,博士生导师,省管优秀专家,研究领域包括可信性测度论、鲁棒优化、最优控制等,在所从事的研究领域中取得了多项代表性研究成果,目前已主持国家自然科学基金面上项目4项;2007年《不确定规划及其应用》项目获得教育部自然科学奖二等奖(排名第二)、2012年《机会测度理论与模糊优化方法》项目获得河北省自然科学奖二等奖(排名第一)、2018年《不确定信息简约理论与参数可信性优化方法》项目获得河北省自然科学奖二等奖(排名第一);出版中、英文学术著作6部,在多家国际知名学术期刊发表SCI/SSCI检索期刊论文70余篇;2014年至2020年连续入选Elsevier中国高被引学者榜单.摘要:鲁棒可信性优化方法是处理模糊可信性分布中包含不确定性的一类有效建模工具.本文综述了近年来鲁棒可信性优化的一些新发展.关于鲁棒可信性优化理论,从垂直和水平波动方向的区分到单参数和双参数选择的设置,回顾了不同波动模式下参数选择变量的定义方法及其与非精确分布集构建的联系.关于鲁棒可信性优化的实践研究,介绍了一些应用问题,如库存、投资、供应链管理以及可持续发展问题,力争提供该方法最新进展的说明并探求未来研究的发展方向. 关键词:鲁棒可信性;选择变量;非精确分布集;应用研究中图分类号:TP183 文献标志码:A 文章编号:1000-1565(2021)05-0457-06Recent advances in robust credibilistic optimizationLIU Yankui, LIU Ying(College of Mathematics and Information Science, Hebei University, Baoding 071002, China )Abstract: Robust credibilistic optimization method is an effective modeling tool to deal with the uncertainty in fuzzy credibility distribution. This paper reviews some new developments of robust credibilistic optimization in recent years. As for the theory of robust credibilistic optimization, this paper reviews the definition of parameter selection variables under different fluctuation modes and their relationship with the construction of ambiguous distribution sets, from the distinction of vertical and horizontal fluctuation directions to the setting of single parameter and double parameter selection. On the practical research of robust credibilistic optimization, we introduce some application problems, such as inventory,- 收稿日期:2021-03-01 基金项目:国家自然科学基金资助项目(61773150) 第一作者:刘彦奎(1963—),男,河北三河人,河北大学教授,博士生导师,主要从事广义测度论、鲁棒优化、最优控制等领域研究. E-mail:yliu@hbu.edu.cn 通信作者:刘颖(1980—),女,河北保定人,河北大学副教授,博士,主要从事不确定优化、供应链管理、项目管理等领域研究. E-mail:yingliu@hbu.edu.cn第5期刘彦奎等:鲁棒可信性优化的新进展investment, supply chain management and sustainable development problem, and strive to provide a description of the latest progress of the method and explore the future research direction.

Key words: robust credibility, selection variable, ambiguous distribution set, application research

CLC Number:

TP183

LIU Yankui, LIU Ying. Recent advances in robust credibilistic optimization[J]. Journal of Hebei University(Natural Science Edition), 2021, 41(5): 457-462.

References

[1] BEN-TAL A, EL GHAOUI L, NEMIROVSKI A. Robust optimization[M]. Princeton: Princeton University Press, 2009. DOI:10.1515/9781400831050.
[2] BIRGE J R, LOUVEAUX F. Multistage stochastic programs[M] //Introduction to Stochastic Programming. New York: Springer, 2011: 265-287. DOI:10.1007/978-1-4614-0237-4_6.
[3] RUSZCZY SKI A, SHAPIRO A. Stochastic programming models[M] //Handbooks in Operations Research and Management Science. Amsterdam: Elsevier, 2003: 1-64. DOI:10.1016/s0927-0507(03)10001-1.
[4] BERTSIMAS D, SIM M. Robust discrete optimization and network flows[J]. Math Program, 2003, 98(1/2/3): 49-71. DOI:10.1007/s10107-003-0396-4.
[5] ZADEH L A. The concept of a linguistic variable and its application to approximate reasoning—I[J]. Inf Sci, 1975, 8(3): 199-249. DOI:10.1016/0020-0255(75)90036-5.
[6] ZADEH L A. Fuzzy sets as a basis for a theory of possibility[J]. Fuzzy Sets Syst, 1978, 1(1): 3-28. DOI:10.1016/0165-0114(78)90029-5.
[7] LIU Y K. Credibility measure theory: An modern methodology of handing subjective uncertainty[M]. Beijing:Science Press, 2018.
[8] 刘彦奎,陈艳菊,刘颖.模糊优化方法与应用[M].北京:科学出版社, 2013.
[9] VAHDANI B, TAVAKKOLI-MOGHADDAM R, JOLAI F. Reliable design of a logistics network under uncertainty: a fuzzy possibilistic-queuing model[J]. Appl Math Model, 2013, 37(5): 3254-3268. DOI:10.1016/j.apm.2012.07.021.
[10] SCARF H. Amin-max solution of an inventory problem. In:Arrow, K.J., Karlin, S., Scarf, H.(eds.). Studies in the mathematical theory of inventory and production[M]. CA: Stanford University Press, 201-209. DOI:10.2307/1910260.
[11] DELAGE E, YE Y Y. Distributionally robust optimization under moment uncertainty with application to data-driven problems[J]. Oper Res, 2010, 58(3): 595-612. DOI:10.1287/opre.1090.0741.
[12] 刘彦奎,刘颖,白雪洁.鲁棒优化方法与应用[M].北京:科学出版社, 2021.
[13] LIU Z Q, LIU Y K. Type-2 fuzzy variables and their arithmetic[J]. Soft Comput, 2010, 14(7): 729-747. DOI:10.1007/s00500-009-0461-x.
[14] LIU Y, LIU Y K. The lambda selections of parametric interval-valued fuzzy variables and their numerical characteristics[J]. Fuzzy Optim Decis Mak, 2016, 15(3): 255-279. DOI:10.1007/s10700-015-9227-3.
[15] LIU Y, GUO Z. Arithmetic about linear combinations of GPIV fuzzy variables[J]. J Uncertain Syst, 2017, 11(2): 154-160.
[16] LIU Y, MA L, LIU Y K. A novel robust fuzzy mean-UPM model for green closed-loop supply chain network design under distribution ambiguity[J]. Appl Math Model, 2021, 92: 99-135. DOI:10.1016/j.apm.2020.10.042.
[17] CHEN Y, SHEN S. The cross selections of parametric interval-valued fuzzy variables[J]. Journal of Uncertain Systems, 2015, 9(2): 156-160.
[18] GUO Z Z, LIU Y K, LIU Y. Coordinating a three level supply chain under generalized parametric interval-valued distribution of uncertain demand[J]. J Ambient Intell Humaniz Comput, 2017, 8(5): 677-694. DOI:10.1007/s12652-017-0472-x.
[19] GUO Z Z, LIU Y K. Modelling single-period inventory problem by distributionally robust fuzzy optimization method[J]. J Intell Fuzzy Syst, 2018, 35(1): 1007-1019. DOI:10.3233/jifs-172128.
[20] PEI H L, LI H L, LIU Y K. Modeling pricing decision problem based on interval type-2 fuzzy theory[J]. J Intell Fuzzy Syst, 2021, 40(6): 11257-11272. DOI:10.3233/jifs-202421.
[21] LIU N Q, CHEN Y J, LIU Y K. Approximating credibilistic constraints by robust counterparts of uncertain linear inequality[J]. Iranian Journal of Fuzzy Systems, 2021, 1-15. DOI:10.22111/IJFS.2021.6075.
[22] GUO Z Z, TIAN S N, LIU Y K. A multiproduct single-period inventory management problem under variable possibility distributions[J]. Math Probl Eng, 2017,2017: 1-14. DOI:10.1155/2017/2159281.
[23] BAI X J, LI X, JIA R R, et al. A distributionally robust credibilistic optimization method for the economic-environmental-energy-social sustainability problem[J]. Inf Sci, 2019, 501: 1-18. DOI:10.1016/j.ins.2019.05.031.
[24] LIU Y, LIU Y K. Distributionally robust fuzzy project portfolio optimization problem with interactive returns[J]. Appl Soft Comput, 2017, 56: 655-668. DOI:10.1016/j.asoc.2016.09.022.
[25] BAI X J, LIU Y K. Robust optimization of supply chain network design in fuzzy decision system[J]. J Intell Manuf, 2016, 27(6): 1131-1149. DOI:10.1007/s10845-014-0939-y.
[26] BAI X J, ZHANG F, LIU Y K. Modeling fuzzy data envelopment analysis under robust input and output data[J]. RAIRO-Oper Res, 2018, 52(2): 619-643. DOI:10.1051/ro/2017038. (