A Neutrosophic Approach Based on TOPSIS Method to Image Segmentation
Keywords:
uncertainty, neutrosophic set, TOPSIS method, FCM, image segmentationAbstract
Neutrosophic set (NS) is a formal framework proposed recently. NS can not only describe the incomplete information in the decision-making system but also depict the uncertainty and inconsistency, so it has applied successfully in several fields such as risk assessment, fuzzy decision and image segmentation. In this paper, a new neutrosophic approach based on TOPSIS method, which can make full use of NS information, is proposed to separate the graphics. Firstly, the image is transformed into the NS domain. Then, two operations, a modified alpha-mean and the beta-enhancement operations are used to enhance image edges and to reduce uncertainty. At last, the segmentation is achieved by the TOPSIS method and the modified fuzzy c-means (FCM). Simulated images and real images are illustrated that the proposed method is more effective and accurate in image segmentation.References
Ali, M.; Smarandache, F. (2017); Complex neutrosophic set, Neural Computing & Applications, 28(7), 1817-1834, 2017. https://doi.org/10.1007/s00521-015-2154-y
Ashraf, M.; Sarim, M.; Shaikh, A.B. (2017). Cellular-Cut-Interactive n-Dimensional Image Segmentation Using Cellular Automata. International Journal of Pattern Recognition & Artificial Intelligence, 2017. https://doi.org/10.1142/S0218001417540179
Bezdek, J.C.; Ehrlich, R.; Full, W. (1984). FCM: The fuzzy c-means clustering algorithm, Computers & Geosciences, 10(2-3), 191-203, 1984. https://doi.org/10.1016/0098-3004(84)90020-7
Cannon, R.L.; Dave, J.V.; Bezdek, J.C. (1986). Efficient Implementation of the Fuzzy c-Means Clustering Algorithms, IEEE Transactions on Pattern Analysis & Machine Intelligence, 8(2), 248-255, 1986. https://doi.org/10.1109/TPAMI.1986.4767778
Chen, L.; Deng, Y. (2018). A new failure mode and effects analysis model using Dempster- Shafer evidence theory and grey relational projection method, Engineering Applications of Artificial Intelligence, 76, 13-20, 2018, doi:10.1016/j.engappai.2018.08.010. https://doi.org/10.1016/j.engappai.2018.08.010
Dempster, A.P. (1967). Upper and Lower Probabilities Induced by a Multi-valued Mapping, Annals of Mathematical Statistics, 38(2),325-339, 1967. https://doi.org/10.1214/aoms/1177698950
Deng, X. (2018). Analyzing the monotonicity of belief interval based uncertainty measures in belief function theory, International Journal of Intelligent Systems, 33(9),1869-1879, 2018. https://doi.org/10.1002/int.21999
Deng, X.; Han, D.; Dezert, J.; Deng, Y.; Shyr, Y. (2016). Evidence combination from an evolutionary game theory perspective, IEEE Transactions on Cybernetics, 46(9), 2070-2082, 2016. https://doi.org/10.1109/TCYB.2015.2462352
Deng, X. Jiang, W. (2018). Dependence assessment in human reliability analysis using an evidential network approach extended by belief rules and uncertainty measures, Annals of Nuclear Energy, 117, 183-193, 2018. https://doi.org/10.1016/j.anucene.2018.03.028
Deng, X.; Jiang, W.; Wang, Z. (2019). Zero-sum polymatrix games with link uncertainty: A Dempster-Shafer theory solution, Applied Mathematics and Computation, 340, 101-112, 2019. https://doi.org/10.1016/j.amc.2018.08.032
Deng X.; Xiao, F.; Deng, Y. (2017). An improved distance-based total uncertainty measure in belief function theory, Applied Intelligence, 46(4), 898-915, 2017. https://doi.org/10.1007/s10489-016-0870-3
Deng, Y. (2012). D numbers: theory and applications, Journal of Information & Computational Science, 9(9), 2421-2428, 2012.
Dou, R.; Nan, G. (2018). Optimizing sensor network coverage and regional connectivity in industrial IoT systems, IEEE Systems Journal, 11(3), 1351-1360, 2018. https://doi.org/10.1109/JSYST.2015.2443045
Eklund, A.; Dufort, P.; Forsberg, D.; Laconte, S.M. (2013). Medical image processing on the GPU: Past, present and future, Medical Image Analysis, 17(17), 1073-1094, 2013. https://doi.org/10.1016/j.media.2013.05.008
Fei, L.; Deng, Y.; Hu, Y. (2018). DS-VIKOR: A New Multi-criteria Decision-Making Method for Supplier Selection, International Journal of Fuzzy Systems, 2018, p. 10.1007/s40815- 018-0543-y.
Greco, S.; Matarazzo, B.; Slowinski, R. (2001). Rough sets theory for multicriteria decision analysis, European Journal of Operational Research, 129(1), 1-47, 2001. https://doi.org/10.1016/S0377-2217(00)00167-3
Guo, Y.; Cheng, H.D. (2009). New neutrosophic approach to image segmentation, Pattern Recognition, 42(5), 587-595, 2009. https://doi.org/10.1016/j.patcog.2008.10.002
Guo, Y.; Sengur, A. (2015). NECM: Neutrosophic evidential c -means clustering algorithm, Neural Computing & Applications, 26(3), 561-571, 2015. https://doi.org/10.1007/s00521-014-1648-3
Guo, Y.; Sengur, A. (2013). A novel color image segmentation approach based on neutrosophic set and modified fuzzy c -means, Circuits, Systems, and Signal Processing, 32(4), 1699-1723, 2013. https://doi.org/10.1007/s00034-012-9531-x
Han, Y.; Deng, Y. (2018). An enhanced fuzzy evidential DEMATEL method with its application to identify critical success factors, Soft computing, 22(15), 5073-5090, 2018. https://doi.org/10.1007/s00500-018-3311-x
He, Z.; Jiang, W. (2018). An evidential Markov decision making model, Information Sciences, 467, 357-372, 2018. https://doi.org/10.1016/j.ins.2018.08.013
He, Z.; Jiang, W. (2018). An evidential dynamical model to predict the interference effect of categorization on decision making, Knowledge-Based Systems, 150, 139-149, 2018. https://doi.org/10.1016/j.knosys.2018.03.014
Hong, C.; Zhang, J.; Cao, X.B.; Du, W.B. (2016). Structural properties of the Chinese air transportation multilayer network, CHAOS SOLITONS & FRACTALS, 86, 28-34, 2016. https://doi.org/10.1016/j.chaos.2016.01.027
Hu, K.; Ye, J.; Fan, E.; Shen, S.; Huang, L.; Pi, J. (2017). A novel object tracking algorithm by fusing color and depth information based on single valued neutrosophic cross-entropy, Journal of Intelligent & Fuzzy Systems, 32(3), 1775-1786, 2017. https://doi.org/10.3233/JIFS-152381
Jiang, W. (2018). A correlation coefficient for belief functions, International Journal of Approximate Reasoning, 2018, p. Published on line, Doi: 10.1016/j.ijar.2018.09.001. https://doi.org/10.1016/j.ijar.2018.09.001
Jiang, W.; Hu, W. (2018). An improved soft likelihood function for Dempster-Shafer belief structures, International Journal of Intelligent Systems, 33(6), 1264-1282, 2018. https://doi.org/10.1002/int.21980
Jiang, W.; Huang, C. (2018). A Multi-criteria Decision-making Model for Evaluating Suppliers in Green SCM, International Journal of Computers Communications & Control, 13(3), 337-352, 2018. https://doi.org/10.15837/ijccc.2018.3.3283
Jiang, W.; Wang, S. (2017). An Uncertainty Measure for Interval-valued Evidences, International Journal of Computers Communications & Control, 12(5), 631-644, 2017. https://doi.org/10.15837/ijccc.2017.5.2950
Kang, B.; Deng, Y.; Hewage, K.; Sadiq, R. (2018). A method of measuring uncertainty for Znumber, IEEE Transactions on Fuzzy Systems, 2018, p. DOI:10.1109/TFUZZ.2018.2868496. https://doi.org/10.1109/TFUZZ.2018.2868496
Kannan, S.R.; Ramathilagam, S.; Devi R.; Hines, E. (2012). Strong fuzzy c-means in medical image data analysis, Journal of Systems and Software, 85(11), 2425-2438, 2012, doi:10.1016/j.jss.2011.12.020. https://doi.org/10.1016/j.jss.2011.12.020
Kittaneh, O.A.; Khan, M.A.U.; Akbar, M.; Bayoud H.A. (2016). Average Entropy: A New Uncertainty Measure with Application to Image Segmentation, American Statistician, 70, 18-24, 2016. https://doi.org/10.1080/00031305.2015.1089788
Kuo, T. (2016). A modified TOPSIS with a different ranking index, European Journal of Operational Research, 260, 2016.
Li, P.; Chen, Z.; Yang, L.T.; Zhao, L.; Zhang, Q. (2017). A privacy-preserving high-order neuro-fuzzy c-means algorithm with cloud computing, Neurocomputing, 2017. https://doi.org/10.1016/j.neucom.2016.08.135
Li, Y.; Deng, Y. (2018). Generalized Ordered Propositions Fusion Based on Belief Entropy, International Journal of Computers Communications & Control, 13(5), 792-807, 2018. https://doi.org/10.15837/ijccc.2018.5.3244
Li, Z.; Chen, L.; Nan, G. (2018). Small-scale Renewable Energy Source Trading: A Contract Theory Approach, IEEE Transactions on Industrial Informatics, 14(4), 1491-1500, 2018. https://doi.org/10.1109/TII.2017.2776241
Liang, W.; He, J.; Wang, S.; Yang, L.; Chen, F. (2018). Improved cluster collaboration algorithm based on wolf pack behavior, Cluster Computing, 2018, p. Published on line, doi: 10.3390/s17040922. https://doi.org/10.3390/s17040922
Lourenzutti, R.; Krohling, R.A.; Reformat, M.Z. (2017). Choquet based TOPSIS and TODIM for dynamic and heterogeneous decision making with criteria interaction, Information Sciences, 408, 41-69, 2017. https://doi.org/10.1016/j.ins.2017.04.037
Mahela, O.P.; Shaik, A.G. (2017). Power quality recognition in distribution system with solar energy penetration using S -transform and Fuzzy C-means clustering, Renewable Energy, 106, 37-51, 2017. https://doi.org/10.1016/j.renene.2016.12.098
Mohan, J.; Krishnaveni, V.; Guo, Y. (2013). MRI denoising using nonlocal neutrosophic set approach of wiener filtering, Biomedical Signal Processing & Control, 8(6), 779-791, 2013. https://doi.org/10.1016/j.bspc.2013.07.005
Muller, H.; Michoux, N.; Bandon, D.; Geissbuhler, A. (2004). A review of content based image retrieval systems in medical applications clinical benefits and future directions, International Journal of Medical Informatics, 73(1), 1-23, 2004. https://doi.org/10.1016/j.ijmedinf.2003.11.024
Nădăban, S.; Dzitac, S. (2016). Neutrosophic TOPSIS: A general view, 2016 6th International Conference on Computers Communications and Control, IEEE, 250-253, 2016.
Nădăban, S.; Dzitac, S.; Dzitac, I. (2016). Fuzzy TOPSIS: A general view, Procedia Computer Science, 91, 823-831, 2016. https://doi.org/10.1016/j.procs.2016.07.088
Nayak, J.; Naik, B.; Behera, H.S.; Abraham, A.(2017);
Hybrid Chemical Reaction based Metaheuristic with Fuzzy c-means Algorithm for Optimal Cluster Analysis, Expert Systems with Applications, 79, 282-295, 2017. https://doi.org/10.1016/j.eswa.2017.02.037
Onu, U.P.; Xie, Q.; Xu, L. (2017). A Fuzzy TOPSIS model Framework for Ranking Sustainable Water Supply Alternatives, Water Resources Management An International Journal Published for the European Water Resources Association, 1-15, 2017.
Peng, J.; Wang, J.; Wu, X.; Wang, J.; Chen, X. (2015). Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decisionmaking Problems, International Journal of Computational Intelligence Systems, 8(2), 345- 363, 2015. https://doi.org/10.1080/18756891.2015.1001957
Qian, P.; Zhao, K.; Jiang, Y.; Su, K.H.; Deng, Z.; Wang, S.; et al. (2017). Knowledgeleveraged transfer fuzzy C -Means for texture image segmentation with self-adaptive cluster prototype matching, Knowledge-Based Systems, 2017.
Reyes-Galaviz, O.F.; Pedrycz, W. (2017). Enhancement of The Classification and Reconstruction Performance of Fuzzy C-Means with Refinements of Prototypes, Fuzzy Sets & Systems, 318, 80-99, 2017. https://doi.org/10.1016/j.fss.2016.07.002
Shafer, G. (1976). A Mathematical Theory of Evidence, New Jersey, Princetion University Press, 1976.
Shan, J.; Cheng, H.D.; Wang, Y. (2012). A novel segmentation method for breast ultrasound images based on neutrosophic l-means clustering, Medical Physics, 39(9), 5669-5682, 2012. https://doi.org/10.1118/1.4747271
Wang, B.; Xiong, H.; Jiang, X.; Zheng, Y.F. (2014). Data-Driven Hierarchical Structure Kernel for Multiscale Part-Based Object Recognition, IEEE Transactions on Image Processing, 23(4), 1765-1778, 2014, doi:10.1109/TIP.2014.2307480. https://doi.org/10.1109/TIP.2014.2307480
Wang, H.; Smarandache, F.; Sunderraman, R.; Zhang, Y.Q. (2005). Interval Neutrosophic Sets and Logic: Theory and Applications in Computing: Theory and Applications in Computing. vol. 5, Infinite Study, 2005.
Wang, H.; Smarandache, F.; Zhang, Y.; Sunderraman, R. (2010). Single valued neutrosophic sets, Rev Air Force Acad, 17, 4-10, 2010.
Wang, P.; Hu, X.; Li, Y.; Liu, Q.; Zhu, X. (2016). Automatic cell nuclei segmentation and classification of breast cancer histopathology images, Signal Processing 122, 1 - 13, 2016. https://doi.org/10.1016/j.sigpro.2015.11.011
Xiao, F. (2019). Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy, Information Fusion, 46(2019), 23-32, 2019;.
Xin, Z.; Shitong, W. (2012). Neutrosophic image segmentation approach based on similarity, Application Research of Computers, 29(6), 2371-2374, 2012.
Xiong, H.; Zheng, D.; Zhu, Q.; Wang, B.; Zheng, Y.F. (2013). A Structured Learning-Based Graph Matching Method for Tracking Dynamic Multiple Objects, IEEE Transactions on Circuits and Systems for Video Technology, 23(3), 534-548, 2013, doi:10.1109/TCSVT.2012.2210801. https://doi.org/10.1109/TCSVT.2012.2210801
Xu, S.; Jiang, W.; Deng, X.; Shou, Y. (2018). A modified Physarum-inspired model for the user equilibrium traffic assignment problem, Applied Mathematical Modelling, 55, 340-353, 2018. https://doi.org/10.1016/j.apm.2017.07.032
Xu, Z.; Hu, C.H.; Yang, F.; Kuo, S.H.; Goh, C.K.; Gupta, A.; et al. (2017). Data-driven Inter-Turn Short Circuit Fault Detection in Induction Machines, IEEE Access, 5(1), 25055- 25068, 2017. https://doi.org/10.1109/ACCESS.2017.2764474
Ye, J. (2013). Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment, International Journal of General Systems, 42(4), 386-394, 2013. https://doi.org/10.1080/03081079.2012.761609
Ye, J. (2014). A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets, Journal of Intelligent & Fuzzy Systems, 26(5), 2459-2466, 2014.
Yin, L.; Deng, Y. (2018). Toward uncertainty of weighted networks: An entropybased model, Physica A: Statistical Mechanics and its Applications, 508, 176-186, 2018, doi:http://doi.org/10.1016/j.physa.2018.05.067. https://doi.org/10.1016/j.physa.2018.05.067
Zadeh, L.A. (2011). A Note on Z-numbers, Information Sciences, 181(14), 2923-2932, 2011. https://doi.org/10.1016/j.ins.2011.02.022
Zhang, G.; Wang, D. (2014). Neutrosophic image segmentation approach integrated LPG & PCA, Journal of Image & Graphics, 19(5), 693-700, 2014.
Zhang, H.; Ji, P.; Wang, J.; Chen, X. (2015). An Improved Weighted Correlation Coefficient Based on Integrated Weight for Interval Neutrosophic Sets and its Application in Multicriteria Decision-making Problems, International Journal of Computational Intelligence Systems, 8(6), 1027-1043, 2015. https://doi.org/10.1080/18756891.2015.1099917
Zhang, M.; Zhang, L.; Cheng, H.D. (2010). A neutrosophic approach to image segmentation based on watershed method, Signal Processing, 90(5), 1510-1517, 2010. https://doi.org/10.1016/j.sigpro.2009.10.021
Zhang, X.; Mahadevan, S. (2017). Aircraft re-routing optimization and performance assessment under uncertainty, Decision Support Systems, 96, 67-82, 2017. https://doi.org/10.1016/j.dss.2017.02.005
Zhang, X.; Mahadevan, S.; Deng, X. (2017). Reliability analysis with linguistic data: An evidential network approach, Reliability Engineering & System Safety, 162, 111-121, 2017. https://doi.org/10.1016/j.ress.2017.01.009
Zhao, X.; Wang, S.T.; Juna, W.U. (2011). Neutrosophic image segmentation approach based on thermal balance, Computer Engineering, 37(19), 210-212, 220, 2011.
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