Multi-Attribute Group Decision Making Algorithm with Probabilistic Dual Hesitant Fuzzy Sets and PROMETHEE Method

doi:10.3778/j.issn.1002-8331.2203-0483

Abstract

Abstract: A multi-attribute group decision-making method based on probabilistic dual hesitant fuzzy sets and the PROMETHEE method is proposed to solve the multi-attribute group decision-making problem in the field of hesitant fuzzy information. Firstly, each decision expert’s probabilistic dual hesitant fuzzy information matrix is constructed. Secondly, the maximum dispersion method and the entropy value method are used to determine the objective weight of each decision-making expert and each index attribute, then the score function and the deviation function are combined to obtain the comprehensive decision-making evaluation information matrix of the decision-making experts. Then, the final decision results are obtained based on the method of combining probabilistic dual hesitant fuzzy sets with PROMETHEE. Finally, the method is applied to the analysis of the case analysis of the emergency response scheme for evaluating the aviation disaster accident, and compared with the calculation results of the TOPSIS, VIKOR, and PDHFS decision-making methods, the validity and reliability of the method have been verified.

Key words: probabilistic dual hesitant fuzzy sets, PROMETHEE method, maximum dispersion, entropy method, multi-attribute group decision

摘要： 为解决犹豫模糊环境中由随机性和不确定性对实际决策造成偏差的多属性群决策问题，提出一种基于概率对偶犹豫模糊PROMETHEE的多属性群决策算法。构建各决策专家的概率对偶犹豫模糊信息矩阵；运用最大离差法与熵值法确定各决策专家与各指标属性的客观权重，结合改进的得分函数与偏离函数得到专家的综合决策评价信息矩阵；进而通过概率对偶犹豫模糊集与PROMETHEE结合的决策算法得到最终决策结果。将该算法运用于航空灾难事故应急响应方案评估的算例分析中，通过与TOPSIS、VIKOR及PDHFS决策算法的计算结果进行对比，验证了概率对偶犹豫模糊PROMETHEE多属性群决策算法的有效性与可靠性。

关键词: 概率对偶犹豫模糊集, PROMETHEE方法, 最大离差法, 熵值法, 多属性群决策

ZHU Yuting, ZHANG Wenyu, HOU Junjie, ZHANG Renjie. Multi-Attribute Group Decision Making Algorithm with Probabilistic Dual Hesitant Fuzzy Sets and PROMETHEE Method[J]. Computer Engineering and Applications, 2022, 58(19): 88-97.

朱钰婷, 张文宇, 侯俊杰, 张仁杰. 概率对偶犹豫模糊PROMETHEE多属性群决策算法[J]. 计算机工程与应用, 2022, 58(19): 88-97.

References

[1] ZADEH L A.Fuzzy sets[J].Information and Control，1965，8（3）：338-353.
[2] ATANASSOV K T.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems，1986，20（1）：87-96.
[3] 李松，袁安琪.考虑直觉模糊的多指标人岗双边匹配决策方法[J].计算机工程与应用，2022，58（12）：304-309.
LI S，YUAN A Q.Method for two-sided matching about personal-job based on multiple criteria considering intuitionistic fuzzy[J].Computer Engineering and Applications，2022，58（12）：304-309.
[4] YAGER R R.Pythagorean membership grades in multicriteria decision making[J].IEEE Transactions on Fuzzy Systems，2014，22（4）：958-965.
[5] 包顺，周礼刚.加型Pythagorean模糊偏好关系的多属性决策方法[J].计算机工程与应用，2021，57（17）：61-67.
BAO S，ZHOU L G.Multiple attribute decision making method based on additive consistent Pythagorean fuzzy preference relations[J].Computer Engineering and Applications，2021，57（17）：61-67.
[6] TORRA V.Hesitant fuzzy sets[J].International Journal of Intelligent Systems，2010，25（6）：529-539.
[7] ALI J，BASHIR Z，TABASAM R.Weighted interval-valued dual-hesitant fuzzy sets and its application in teaching quality assessment[J].Soft Computing，2021，25：3503-3530.
[8] 冯锋，万喆，徐泽水，等.基于软粗糙集的犹豫模糊三支决策方法[J/OL].控制与决策：1-9[2022-03-23].DOI：10.13195/j.kzyjc.2021.1662.
FENG F，WAN Z，XU Z S，et al.Hesitant fuzzy three-way decision method based on soft rough sets[J/OL].Control and Decision：1-9[2022-03-23].DOI：10.13195/j.kzyjc.2021.1662.
[9] ZHU B，XU Z S，XIA M M.Dual hesitant fuzzy sets[J].Journal of Applied Mathematics，2012，2012：2607-2645.
[10] XU Z S，ZHOU W.Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment[J].Fuzzy Optimization and Decision Making，2017，16：481-503.
[11] HAO Z N，XU Z S，ZHAO H，et al.Probabilistic dual hesitant fuzzy set and its application in risk evaluation[J].Knowledge-Based Systems，2017，127：16-28.
[12] GARG H，KAUR G.A robust correlation coefficient for probabilistic dual hesitant fuzzy sets and its applications[J].Neural Computing and Applications，2020，32（4）：8847-8866.
[13] BRANS J P，VINCKE P.Note—A preference ranking organisation method[J].Management Science，1985，31（6）：647-656.
[14] 刘利枚，龚尹励，曹文治，等.基于语言区间直觉模糊幂加权平均算子的多属性群决策方法[J].模糊系统与数学，2021，35（4）：124-135.
LIU L M，GONG Y L，CAO W Z，et al.Multi-attribute group decision-making method based on linguistic interval-valued intuitionistic fuzzy power weighted average operator[J].Fuzzy Systems and Mathematics，2021，35（4）：124-135.
[15] 谢小军，马虹，朱宁，等.基于区间相似度IOWGA算子的三角模糊数组合预测模型[J].统计与决策，2020，36（23）：23-27.
XIE X J，MA H，ZHU N，et al.A triangular fuzzy number combination forecasting model of IOWGA operator based on interval similarity[J].Statistics and Decision Making，2020，36（23）：23-27.
[16] 徐泽水，罗书琴，廖虎昌.概率语言PROMETHEE方法及其在医疗服务中的应用[J].系统工程学报，2019，34（6）：760-769.
XU Z S，LUO S Q，LIAO H C.Probabilistic linguistic PROMETHEE method and its application in medical service[J].Journal of Systems Engineering，2019，34（6）：760-769.
[17] 赵晓冬，张妮.犹豫中智语言PROMETHEE方法在网络谣言管控方案评选中的应用[J].模糊系统与数学，2021，35（3）：78-90.
ZHAO X D，ZHANG N.A hesitant neutrosophic linguistic PROMETHEE method and it application in evaluation of network rumor management scheme[J].Fuzzy Systems and Mathematics，2021，35（3）：78-90.
[18] 朱江洪，李延来，王睿.基于前景理论与PROMETHEE的FMEA风险评估[J].运筹与管理，2018，27（12）：147-157.
ZHU J H，LI Y L，WANG R.Risk assessment of FMEA based on prospect theory and PROMETHEE[J].Operations Research and Management Science，2018，27（12）：147-157.
[19] 于弘泽，朱钰婷，治瑜，等.基于区间Pythagorean-PROMETHEE算法的水资源配置方案多属性群决策[J/OL].中国农村水利水电：1-15（2022-01-19）[2022-03-23].http：//kns.cnki.net/kcms/detail/42.1419.TV.20220119.1301.037.html.
YU H Z，ZHU Y T，ZHI Y，et al.Multi-attribute group decision making for water allocation scheme based on interval Pythagorean?PROMETHEE algorithm[J/OL].China Rural Water and Hydropower：1-15（2022-01-19）[2022-03-23].http：//kns.cnki.net/kcms/detail/42.1419.TV.20220119.
1301.037.html.
[20] REN Z L，XU Z S，WANG H.Dual hesitant fuzzy VIKOR method for multi-criteria group decision making based on fuzzy measure and new comparison method[J].Information Sciences，2017，388/389：1-16.
[21] XIE W Y，REN Z N，XU Z S，et al.The consensus of probabilistic uncertain linguistic preference relations and the application on the virtual reality industry[J].Knowledge-Based Systems，2018，162：14-28.
[22] 耿秀丽，邱华清.基于犹豫模糊PROMETHEE[Ⅱ]的设计方案群决策方法[J].计算机应用研究，2018，35（10）：3020-3024.
GENG X L，QIU H Q，Group decision-making method of design concept based on hesitant fuzzy PROMETHEE [Ⅱ][J].Application Research of Computers，2018，35（10）：3020-3024.
[23] BRANS J P，MARESCHAL B，FIGUEIRA J，et al.Promethee methods[J].Multiple Criteria Decision Analysis State of the Art Surveys，2005，78：163-186.
[24] 李翔晨.最大离差与熵法在导弹预警系统作战效能评估中的应用[J].中国电子科学研究院学报，2020，15（3）：284-288.
LI X C.Application of maximum deviations and entropy to effectiveness evaluation of missile early warning system[J].Journal of China Academy of Electronics and Information Technology，2020，15（3）：284-288.
[25] 叶雪强，桂预风.基于Markov链修正的改进熵值法组合模型及应用[J].统计与决策，2018，34（2）：69-72.
YE X Q，GUI Y F.Markov chain-based improved entropy method combined model and its application[J].Statistics and Decision，2018，34（2）：69-72.
[26] 臧誉琪.区间犹豫模糊环境下的多属性决策方法及应用研究[D].秦皇岛：燕山大学，2018.
ZANG Y Q.Research on multi-attribute decision making method and application in interval hesitant fuzzy environment[D].Qinhuangdao：Yanshan University，2018.
[27] 王应明，阙翠平，蓝以信.基于前景理论的犹豫模糊TOPSIS多属性决策方法[J].控制与决策，2017，32（5）：864-870.
WANG Y M，QUE C P，LAN Y X.Hesitant fuzzy TOPSIS multi-attribute decision method based on prospect theory[J].Control and Decision，2017，32（5）：864-870.
[28] 陈秀明，刘业政.基于熵权的多粒度犹豫模糊语言VIKOR群推荐方法[J].控制与决策，2018，33（1）：111-118.
CHEN X M，LIU Y Z.Multi-granular hesitant fuzzy linguistic term sets and their application in group recommendation based on entropy measure and VIKOR method[J].Control and Decision，2018，33（1）：111-118.
[29] RONG Y，LIU Y，PEI Z.A novel multiple attribute decision-making approach for evaluation of emergency management schemes under picture fuzzy environment[J].International Journal of Machine Learning and Cybernetics，2022，13：633-661.
[30] VASUANINCHITA M，VONGMANEE V，RATTANAWONG W.The novel paradigm of economics driven for local smart sustain cities modeling using exploratory factor analysis and planning technique using fuzzy evaluation decision making[J].Sustainability，2020，12（3）：1-20.
[31] HOSSEINI F S，SIGAROODI S K，SALAJEGHEH A，et al.Towards a flood vulnerability assessment of watershed using integration of decision making trial and evaluation laboratory，analytical network process，and fuzzy theories[J].Environmental Science and Pollution Research，2021，28：62487-62498.