|
|
|
| Multiple-Attribute Decision-Making Method Based on Correlation Coefficient of Probabilistic Dual Hesitant Fuzzy Information with Unknown Weights of Attribute |
| SONG Juan1,2, NI Zhiwei1,2, WU Wenying1,2, JIN Feifei3, LI Ping1,2,4 |
1. School of Management, Hefei University of Technology, Hefei 230009;
2. Key Laboratory of Process Optimization and Intelligent Decision-Making, Ministry of Education, Hefei University of Tech-nology, Hefei 230009;
3. School of Business, Anhui University, Hefei 230601;
4. College of Information Engineering, Fuyang Normal University, Fuyang 236041 |
|
|
|
|
Abstract The probabilistic dual hesitant fuzzy set contains membership degree, non-membership degree and their corresponding probability information. It is an important tool to describe uncertain decision-making information. To solve the probabilistic dual hesitant fuzzy multiple-attribute decision-making problem with unknown attribute weight information, a multiple-attribute decision-making method is proposed based on the correlation coefficient of probabilistic dual hesitant fuzzy information. Firstly, the objective attribute weight is calculated by probabilistic dual hesitant fuzzy information entropy and combined with the subjective attribute weight given by decision-maker to obtain the comprehensive weight of attribute. Secondly, a correlation coefficient and a weighted correlation coefficient are proposed to measure the correlation level between decision-making information, and the excellent properties of the proposed correlation coefficients are analyzed. Finally, a multi-attribute decision-making method based on the correlation coefficient of probabilistic dual hesitant fuzzy information is designed and applied to the selection experiment of haze control strategies. Experimental results show that the proposed method produces good robustness and effectiveness.
|
|
Received: 01 September 2021
|
|
|
| Fund:National Natural Science Foundation of China(No.91546108,71901001,61806068,71521001), Natural Science Foundation of Anhui Province(No.2008085QG333), Key Research Project of Natural Science in Colleges and Universities of Anhui Province(No.KJ2021A1253), Key Research Project of Humanities and Social Sciences in Colleges and Universities of Anhui Province(No.SK2020A0038) |
|
Corresponding Authors:
NI Zhiwei, Ph.D., professor. His research interests include machine learning, intelligent management and big data.
|
| About author:: SONG Juan, Ph.D. candidate. Her research interests include intelligent management and decision analysis. WU Wenying, Ph.D. candidate. Her research interests include fuzzy decision ma-king. JIN Feifei, Ph.D., associate professor. His research interests include intelligent ma-nagement and decision analysis. LI Ping, Ph.D., lecturer. Her research interests include pattern recognition and machine learning. |
|
|
|
[1] 韩进,施龙青,翟培合,等.多属性决策及D-S证据理论在底板突水决策中的应用.岩石力学与工程学报, 2009, 28(S2): 3727-3732.
(HAN J, SHI L Q, ZHAI P H, et al. Application of Multi-attribute Decision and D-S Evidence Theory to Water-Inrush Decision of Floor in Mining. Chinese Journal of Rock Mechanics and Engineering, 2009, 28(S2): 3727-3732.)
[2] 陈建中,徐玖平.群决策的交互式TOPSIS方法及其应用.系统工程学报, 2008, 23(3): 276-281, 346.
(CHEN J Z, XU J P. TOPSIS Based Interactive Multi-attributes Group Decision-Making Method and Its Application. Journal of Systems Engineering, 2008, 23(3): 276-281, 346.)
[3] MOJTAHEDI S M, MOUSAVI S M, MAKUI A. Project Risk Identification and Assessment Simultaneously Using Multi-attribute Group Decision Making Technique. Safety Science, 2010, 48(4): 499-507.
[4] WHEELER J, PÁEZ M A, GUILLÉN-GOSÁLBEZ G, et al. Combining Multi-attribute Decision-Making Methods with Multi-objective Optimization in the Design of Biomass Supply Chains. Computers & Chemical Engineering, 2018, 113: 11-31.
[5] GOVINDAN K, SIVAKUMAR R. Green Supplier Selection and Order Allocation in a Low-Carbon Paper Industry: Integrated Multi-criteria Heterogeneous Decision-Making and Multi-objective Linear Programming Approaches. Annals of Operations Research, 2016, 238: 243-276.
[6] 刘海涛,郭嗣琮.基于结构元理论的模糊多属性群决策方法.模式识别与人工智能, 2007, 20(3): 343-348.
(LIU H T, GUO S Z. Fuzzy Multi-attribute Group Decision Making Methods Based on Structured Element. Pattern Recognition and Artificial Intelligence, 2007, 20(3): 343-348.)
[7] SHEN L X, OLFAT L, GOVINDAN K, et al. A Fuzzy Multi Criteria Approach for Evaluating Green Supplier's Performance in Green Supply Chain with Linguistic Preferences. Resources, Conservation and Recycling, 2013, 74: 170-179.)
[8] 龚艳冰,梁雪春.基于模糊C-OWA算子的模糊多属性决策方法.系统工程与电子技术, 2008, 30(8): 1478-1480.
(GONG Y B, LIANG X C. Fuzzy Multi-attribute Decision Making Method Based on Fuzzy C-OWA Operator. Systems Engineering and Electronics, 2008, 30(8): 1478-1480.)
[9] KUO T C, CHANG S H, HUANG S H. Environmentally Conscious Design by Using Fuzzy Multi-attribute Decision-Making. The International Journal of Advanced Manufacturing Technology, 2006, 29: 419-425.
[10] ASHRAF S, ABDULLAH S, ASLAM M. Symmetric Sum Based Aggregation Operators for Spherical Fuzzy Information: Application in Multi-attribute Group Decision Making Problem. Journal of Intelligent & Fuzzy Systems, 2020, 38(4): 5241-5255.
[11] ATANASSOV K T. Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 1986, 20(1): 87-96.
[12] 张亮,王坚浩,郑东良,等.基于直觉模糊熵和VIKOR的装备器材供应商选优决策.系统工程与电子技术, 2019, 41(7): 1568-1575.
(ZHANG L, WANG J H, ZHENG D L, et al. Equipment Material Suppliers Selection Decision-Making Based on Intuitionistic Fuzzy Entropy and VIKOR. Systems Engineering and Electronics, 2019, 41(7): 1568-1575.)
[13] WANG H B, SMARANDACHE F, ZHANG Y Q, et al. Single Valued Neutrosophic Sets[C/OL]. [2021-08-10]. http://fs.unm.edu/SingleValuedNeutrosophicSets.pdf.
[14] 范建平,刘胜男,吴美琴.单值Neutrosophic sets环境下基于参照系数的VIKOR方法.中国管理科学, 2019, 27(6): 136-145.
(FAN J P, LIU S N, WU M Q. VIKOR Method Based on the Re-ference Coefficient under Single-Valued Neutrosophic Environment. Chinese Journal of Management Science, 2019, 27(6): 136-145.)
[15] BROUMI S, TALEA M, BAKALI A, et al. Shortest Path Problem in Fuzzy, Intuitionistic Fuzzy and Neutrosophic Environment: An Overview. Complex & Intelligent Systems, 2019, 5: 371-378.
[16] GUO J P, DENG J Z, WANG Y. An Intuitionistic Fuzzy Set Based Hybrid Similarity Model for Recommender System. Expert Systems with Applications, 2019, 135: 153-163.
[17] BASHAN V, DEMIREL H, GUL M. An FMEA-Based TOPSIS App-roach under Single Valued Neutrosophic Sets for Maritime Risk Evaluation: The Case of Ship Navigation Safety. Soft Computing, 2020, 24: 18749-18764.
[18] WAN S P, JIN Z, DONG J Y. A New Order Relation for Pythagorean Fuzzy Numbers and Application to Multi-attribute Group Decision Making. Knowledge and Information Systems, 2020, 62(2): 751-785.
[19] LIU C F, LUO Y S. Power Aggregation Operators of Simplified Neutrosophic Sets and Their Use in Multi-attribute Group Decision Making. IEEE/CAA Journal of Automatica Sinica, 2019, 6(2): 575-583.
[20] 刘久兵,王天行,周献中,等.基于勾股模糊集评价的三支决策方法.模式识别与人工智能, 2019, 32(12): 1080-1092.
(LIU J B, WANG T X, ZHOU X Z, et al. Three-Way Decisions Method Based on Evaluations of Pythagorean Fuzzy Sets. Pattern Recognition and Artificial Intelligence, 2019, 32(12): 1080-1092.)
[21] LIN M W, HUANG C, CHEN R Q, et al. Directional Correlation Coefficient Measures for Pythagorean Fuzzy Sets: Their Applications to Medical Diagnosis and Cluster Analysis. Complex & Inte-lligent Systems, 2021, 7(2): 1025-1043.
[22] BAKIOGLU G, ATAHAN A O. AHP Integrated TOPSIS and VIKOR Methods with Pythagorean Fuzzy Sets to Prioritize Risks in Self-Driving Vehicles. Applied Soft Computing, 2021, 99. DOI: 10.1016/j.asoc.2020.106948.
[23] TORRA V. Hesitant Fuzzy Sets. International Journal of Intelligent Systems, 2010, 25(6): 529-539.
[24] ZHU B, XU Z S, XIA M M. Dual Hesitant Fuzzy Sets. Journal of Applied Mathematics, 2012. DOI: 10.1155/2012/879629.
[25] 朱斌.基于偏好关系的决策方法及应用研究.博士学位论文.南京:东南大学, 2014.
(ZHU B. Decision Method for Research and Application Based on Preference Relation. Ph. D. Dissertation. Nanjing, China: Southeast University, 2014.)
[26] KRISHANKUMAR R, RAVICHANDRAN K S, KAR S, et al. Double-Hierarchy Hesitant Fuzzy Linguistic Term Set-Based Decision Framework for Multi-attribute Group Decision-Making. Soft Computing, 2021, 25: 2665-2685.
[27] ZHENG Y F, XU J, CHEN H Z. TOPSIS-Based Entropy Measure for Intuitionistic Trapezoidal Fuzzy Sets and Application to Multi-attribute Decision Making. Mathematical Biosciences and Engineering, 2020, 17(5): 5604-5617.
[28] WANG X K, WANG J Q, ZHANG H Y. Distance-Based Multicriteria Group Decision-Making Approach with Probabilistic Linguistic Term Sets. Expert Systems, 2019, 36(2). DOI: 10.1111/exsy.12352.
[29] 向南,豆亚杰,姜江,等.基于专家信任网络的不完全信息武器选择决策.系统工程理论与实践, 2021, 40(3): 759-770.
(XIANG N, DOU Y J, JIANG J, et al. Weapon Selection Decision-Making Based on Expert Trust Network under Incomplete Information. Systems Engineering-Theory & Practice, 2021, 40(3): 759-770.)
[30] SONG C Y, XU Z S, ZHAO H. New Correlation Coefficients Between Probabilistic Hesitant Fuzzy Sets and Their Applications in Cluster Analysis. International Journal of Fuzzy Systems, 2019, 21(2): 355-368.
[31] MENG F Y, XU Y W, WANG N. Correlation Coefficients of Dual Hesitant Fuzzy Sets and Their Application in Engineering Management. Journal of Ambient Intelligence and Humanized Computing, 2020, 11(7): 2943-2961.
[32] 曾守桢,骆丹丹.基于类Pearson综合相关系数的概率语言TOP-SIS多属性决策方法.系统科学与数学, 2021, 41(1): 126-143.
(ZENG S Z, LUO D D. A Pearson-Like Synthetic Correlation-Based TOPSIS Multiple Attribute Decision-Making Approach for Probabilistic Linguistic Term Information. Journal of Systems Science and Mathematical Sciences, 2021, 41(1): 126-143.)
[33] LI S L, WEI C P. Hesitant Fuzzy Linguistic Correlation Coefficient and Its Applications in Group Decision Making. International Journal of Fuzzy Systems, 2020, 22(6): 1748-1759.
[34] SUN G D, GUAN X, YI X, et al. Improvements on Correlation Coefficients of Hesitant Fuzzy Sets and Their Applications. Cognitive Computation, 2019, 11(4): 529-544.
[35] HAO Z N, XU Z S, ZHAO H, et al. Probabilistic Dual Hesitant Fuzzy Set and Its Application in Risk Evaluation. Knowledge-Based Systems, 2017, 127: 16-28.
[36] GARG H, KAUR G. Algorithms for Screening Travelers During COVID-19 Outbreak Using Probabilistic Dual Hesitant Values Based on Bipartite Graph Theory. Applied and Computational Mathematics, 2021, 20(1): 22-48.
[37] GARG H, KAUR G. A Robust Correlation Coefficient for Probabilistic Dual Hesitant Fuzzy Sets and Its Applications. Neural Computing and Applications, 2020, 32: 8847-8866.
[38] GARG H, KAUR G. Quantifying Gesture Information in Brain Hemorrhage Patients Using Probabilistic Dual Hesitant Fuzzy Sets with Unknown Probability Information. Computers & Industrial Engineering, 2020, 140. DOI: 10.1016/j.cie.2019.106211.
[39] REN Z L, XU Z S, WANG H. The Strategy Selection Problem on Artificial Intelligence with an Integrated VIKOR and AHP Method under Probabilistic Dual Hesitant Fuzzy Information. IEEE Access, 2019, 7: 103979-103999.
[40] GARG H, KAUR G. Algorithm for Probabilistic Dual Hesitant Fuzzy Multi-criteria Decision-Making Based on Aggregation Operators with New Distance Measures. Mathematics, 2018, 6(12): 280-309.
[41] ZHAO Q, JU Y B, PEDRYCZ W. A Method Based on Bivariate Almost Stochastic Dominance for Multiple Criteria Group Decision Making with Probabilistic Dual Hesitant Fuzzy Information. IEEE Access, 2020, 8: 203769-203786. |
|
|
|
2022, Vol. 35 
