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| Hesitant Fuzzy Graph and Its Application to Multi-attribute Decision Making |
| ZHANG Chao, LI Deyu |
| 1.Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education,School of Computer and Information Technology, Shanxi University, Taiyuan 030006 |
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Abstract As an effective tool for describing indecisiveness quantitatively, hesitant fuzzy sets deal with the hesitation and the fuzziness in uncertain information simultaneously to solve multi-attribute decision making problems under the background of indecisiveness. Aiming at multi-attribute decision making problems with hesitant fuzzy attribute values, the related model and the multi-attribute decision making approach based on the fuzzy graph theory are studied. Firstly, the concept of hesitant fuzzy graph and some common operational laws are presented. Then, a general hesitant fuzzy graph-based multi-attribute decision making method is established. Finally, an illustrative example and the comparative analysis are conducted to verify the feasibility of the proposed method.
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Received: 15 March 2017
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| Fund:Supported by National Natural Science Foundation of China(No.61672331,61573231,61432011,U1435212,61303107,61272095), Natural Science Foundation of Shanxi Province(No.201601D021076,201601D021072,2015021101,2015091001-0102) |
About author:: 张 超,男,1989年生,博士,讲师,主要研究方向为智能优化计算、粒计算.E-mail:zhch3276152@163.com.
李德玉(通讯作者),男,1965年生,博士,教授,主要研究方向为粒计算、机器学习.E-mail:lidysxu@163.com. |
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[1] ZADEH L A. Fuzzy Logic-A Personal Perspective. Fuzzy Sets and Systems, 2015, 281: 4-20.
[2] BUSTINCE H, BARRENECHEA E, PAGOLA M, et al. A Historical Account of Types of Fuzzy Sets and Their Relationships. IEEE Transactions on Fuzzy Systems, 2015, 24(1): 179-194.
[3] TORRA V. Hesitant Fuzzy Sets. International Journal of Intelligent Systems, 2010, 25(6): 529-539.
[4] XIA M M, XU Z S. Hesitant Fuzzy Information Aggregation in Decision Making. International Journal of Approximate Reasoning, 2011, 52(3): 395-407.
[5] CHEN N, XU Z S, XIA M M. Correlation Coefficients of Hesitant Fuzzy Sets and Their Applications to Clustering Analysis. Applied Mathematical Modelling, 2013, 37(4): 2197-2211.
[6] YANG X B, SONG X N, QI Y S, et al. Constructive and Axiomatic Approaches to Hesitant Fuzzy Rough Set. Soft Computing, 2014, 18(6): 1067-1077.
[7] ZHANG C, LI D Y, YAN Y. A Dual Hesitant Fuzzy Multigranulation Rough Set over Two-Universe Model for Medical Diagnoses. Computational and Mathematical Methods in Medicine, 2015. DOI: 10.1155/2015/292710.
[8] 张小路.基于犹豫模糊信息的多属性决策方法研究.博士学位论文.南京:东南大学, 2015.
(ZHANG X L. Research on Multiple Attribute Decision Making Methods with Hesitant Fuzzy Information. Ph. D Dissertation. Nanjing, China: Southeast University, 2015.)
[9] 王宝丽,梁吉业,胡运红.基于粒计算的犹豫模糊多准则决策方法.模式识别与人工智能, 2016, 29(3): 252-262.
(WANG B L, LIANG J Y, HU Y H. Granular Computing Based Hesitant Fuzzy Multi-criteria Decision Making. Pattern Recognition and Artificial Intelligence, 2016, 29(3): 252-262.)
[10] ZHANG C, LI D Y, Mu Y M, et al. An Interval-Valued Hesitant Fuzzy Multigranulation Rough Set over Two Universes Model for Steam Turbine Fault Diagnosis. Applied Mathematical Modeling, 2017, 42: 693-704.
[11] 张 超,李德玉,翟岩慧.双论域上的犹豫模糊语言多粒度粗糙集及其应用.控制与决策, 2017, 32(1): 105-110.
(ZHANG C, LI D Y, ZHAI Y H. Hesitant Fuzzy Linguistic Multigranulation Rough Set over Two Universes and Its Application. Control and Decision, 2017, 32(1): 105-110.)
[12] GARMENDIA L, DEL CAMPO R G, RECASENS J. Partial Or-derings for Hesitant Fuzzy Sets. International Journal of Approximate
Reasoning, 2017, 84: 159-167.
[13] ROSENFELD A. Fuzzy Graphs // ZADEH L A, FU K S, SHIMURA M, eds. Fuzzy Sets and Their Applications. New York, USA: Academic Press, 1975: 77-95.
[14] MORDESON J N, PENG C S. Operations on Fuzzy Graphs. Information Sciences, 1994, 79(3/4): 159-170.
[15] BHUTANI K R, BATTOU A. On M-strong Fuzzy Graphs. Information Sciences, 2003, 155(1/2): 103-109.
[16] AKRAM M, DUDEK W A. Interval-Valued Fuzzy Graphs. Computers & Mathematics with Applications, 2011, 61(2): 289-299.
[17] 杨文华,李生刚.区间值模糊图的运算性质.模糊系统与数学, 2013, 27(2): 127-135.
(YANG W H, LI S G. Operation Properties of Interval-Valued Fuzzy Graphs. Fuzzy Systems and Mathematics, 2013, 27(2): 127-135.)
[18] 索南仁欠,李生刚.区间值强模糊图的运算性质.计算机工程与应用, 2014, 50(17): 12-15.
(SUONAN R Q, LI S G. Strong Interval Value Fuzzy Operation Properties of Graph. Computer Engineering and Applications, 2014, 50(17): 12-15.)
[19] SINGH P K, KUMAR C A. Bipolar Fuzzy Graph Representation of Concept Lattice. Information Sciences, 2014, 288: 437-448.
[20] DRAKOPOULOS G, GOURGARIS P, KANAVOS A, et al. A Fuzzy Graph Framework for Initializing K-means. International Journal on Artificial Intelligence Tools, 2016, 25(6): 165-186.
[21] SAMANTA S, PAL M. Fuzzy Planar Graphs. IEEE Transactions on Fuzzy Systems, 2015, 23(6): 1936-1942.
[22] RASHMANLOU H, SAMANTA S, PAL M, et al. Product of Bipolar Fuzzy Graphs and Their Degree. International Journal of Gene-ral Systems, 2016, 45(1). DOI: 10.1080/03081079.2015.1072521.
[23] MATHEW S, MORDESON J N. Connectivity Concepts in Fuzzy Incidence Graphs. Information Sciences, 2017, 382/383: 326-333. |
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2017, Vol. 30 
