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Sevcan Yilmaz Gunduz


Breast cancer is one of the most common types of cancer. For this reason, it is very important to diagnose breast cancer. In this paper, a type-2 fuzzy multiplication wavelet neural network model is proposed to classify the Wisconsin Breast Cancer dataset. In this model, Shannon wavelet function is used as the type-2 membership function and the multiplication of the Shannon wavelet functions is used in the conclusion part of the rules. The results of proposed model is compared with type-1 fuzzy multiplication wavelet neural network, multilayer perceptron network, radial basis function network, Bayesian network learning, and decision tree algorithm. It can be seen that proposed type-2 fuzzy multiplication wavelet neural network model gives the best results among these algorithms.


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T. S. Subashini, V. Ramalingam, and S. Palanivel, "Breast mass classification based on cytological patterns using RBFNN and SVM," Expert Systems with Applications, vol. 36, pp. 5284-5290, Apr 2009.

M. Karabatak and M. C. Ince, "An expert system for detection of breast cancer based on association rules and neural network," Expert Systems with Applications, vol. 36, pp. 3465-3469, Mar 2009.

M. R. Mohebian, H. R. Marateb, M. Mansourian, M. A. Mananas, and F. Mokarian, "A Hybrid Computer-aided-diagnosis System for Prediction of Breast Cancer Recurrence (HPBCR) Using Optimized Ensemble Learning," Computational and Structural Biotechnology Journal, vol. 15, pp. 75-85, 2017.

T. Ince, S. Kiranyaz, J. Pulkkinen, and M. Gabbouj, "Evaluation of global and local training techniques over feed-forward neural network architecture spaces for computer-aided medical diagnosis," Expert Systems with Applications, vol. 37, pp. 8450-8461, Dec 2010.

T. Nguyen, A. Khosravi, D. Creighton, and S. Nahavandi, "Medical data classification using interval type-2 fuzzy logic system and wavelets," Applied Soft Computing, vol. 30, pp. 812-822, May 2015.

T. Nguyen, A. Khosravi, D. Creighton, and S. Nahavandi, "Classification of healthcare data using genetic fuzzy logic system and wavelets," Expert Systems with Applications, vol. 42, pp. 2184-2197, Mar 2015.

A. Ghosh, B. C. Dhara, and R. K. De, "Selection of genes mediating certain cancers, using a neuro-fuzzy approach," Neurocomputing, vol. 133, pp. 122-140, Jun 10 2014.

N. Leema, H. K. Nehemiah, and A. Kannan, "Neural network classifier optimization using Differential Evolution with Global Information and Back Propagation algorithm for clinical datasets," Applied Soft Computing, vol. 49, pp. 834-844, Dec 2016.

S. Horikawa, T. Furuhashi, and Y. Uchikawa, "On Fuzzy Modeling Using Fuzzy Neural Networks with the Backpropagation Algorithm," IEEE Transactions on Neural Networks, vol. 3, pp. 801-806, Sep 1992.

J. S. R. Jang, "Anfis - Adaptive-Network-Based Fuzzy Inference System," IEEE Transactions on Systems Man and Cybernetics, vol. 23, pp. 665-685, May-Jun 1993.

C. F. Juang and C. T. Lin, "An on-line self-constructing neural fuzzy inference network and its applications," IEEE Transactions on Fuzzy Systems, vol. 6, pp. 12-32, Feb 1998.

J. Kim and N. Kasabov, "HyFIS: adaptive neuro-fuzzy inference systems and their application to nonlinear dynamical systems," Neural Networks, vol. 12, pp. 1301-1319, Nov 1999.

G. J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic Theory and Applications: Prentice Hall, 1995.

O. Castillo and P. Melin, Type-2 Fuzzy Logic: Theory and Applications vol. 223: Springers Berlin Heidelberg, 2008.

Q. L. Liang and J. M. Mendel, "Interval type-2 fuzzy logic systems: Theory and design," IEEE Transactions on Fuzzy Systems, vol. 8, pp. 535-550, Oct 2000.

R. A. Aliev, W. Pedrycz, B. G. Guirimov, R. R. Aliev, U. Ilhan, M. Babagil, et al., "Type-2 fuzzy neural networks with fuzzy clustering and differential evolution optimization," Information Sciences, vol. 181, pp. 1591-1608, May 1 2011.

J. R. Castro, O. Castillo, P. Melin, and A. Rodriguez-Diaz, "A hybrid learning algorithm for a class of interval type-2 fuzzy neural networks," Information Sciences, vol. 179, pp. 2175-2193, Jun 13 2009.

C. F. Juang and Y. W. Tsao, "A Self-Evolving Interval Type-2 Fuzzy Neural Network With Online Structure and Parameter Learning," IEEE Transactions on Fuzzy Systems, vol. 16, pp. 1411-1424, Dec 2008.

G. M. Mendez and M. D. Hernandez, "Hybrid learning mechanism for interval A2-C1 type-2 non-singleton type-2 Takagi-Sugeno-Kang fuzzy logic systems," Information Sciences, vol. 220, pp. 149-169, Jan 20 2013.

S. W. Tung, C. Quek, and C. Guan, "eT2FIS: An Evolving Type-2 Neural Fuzzy Inference System," Information Sciences, vol. 220, pp. 124-148, Jan 20 2013.

C. H. Wang, C. S. Cheng, and T. T. Lee, "Dynamical optimal training for interval type-2 fuzzy neural network (T2FNN)," IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics, vol. 34, pp. 1462-1477, Jun 2004.

R. H. Abiyev, O. Kaynak, and E. Kayacan, "A type-2 fuzzy wavelet neural network for system identification and control," Journal of the Franklin Institute-Engineering and Applied Mathematics, vol. 350, pp. 1658-1685, Sep 2013.

F. J. Lin and P. H. Chou, "Adaptive Control of Two-Axis Motion Control System Using Interval Type-2 Fuzzy Neural Network," IEEE Transactions on Industrial Electronics, vol. 56, pp. 178-193, Jan 2009.

J. R. Castro, O. Castillo, P. Melin, O. Mendoza, and A. Rodriguez-Diaz, "An Interval Type-2 Fuzzy Neural Network for Chaotic Time Series Prediction with Cross-Validation and Akaike Test," in Soft Computing for Intelligent Control and Mobile Robotics. vol. 318, ed, 2011, pp. 269-285.

M. Singh, S. Srivastava, M. Hanmandlu, and J. R. P. Gupta, "Type-2 fuzzy wavelet networks (T2FWN) for system identification using fuzzy differential and Lyapunov stability algorithm," Applied Soft Computing, vol. 9, pp. 977-989, Jun 2009.

C. Y. Yeh, W. H. R. Jeng, and S. J. Lee, "Data-Based System Modeling Using a Type-2 Fuzzy Neural Network with a Hybrid Learning Algorithm," IEEE Transactions on Neural Networks, vol. 22, pp. 2296-2309, Dec 2011.

C. F. Liu, C. Y. Yeh, and S. J. Lee, "Application of type-2 neuro-fuzzy modeling in stock price prediction," Applied Soft Computing, vol. 12, pp. 1348-1358, Apr 2012.

O. Castillo, R. Martinez-Marroquin, P. Melin, F. Valdez, and J. Soria, "Comparative study of bio-inspired algorithms applied to the optimization of type-1 and type-2 fuzzy controllers for an autonomous mobile robot," Information Sciences, vol. 192, pp. 19-38, Jun 1 2012.

P. Melin, L. Astudillo, O. Castillo, F. Valdez, and M. Garcia, "Optimal design of type-2 and type-1 fuzzy tracking controllers for autonomous mobile robots under perturbed torques using a new chemical optimization paradigm," Expert Systems with Applications, vol. 40, pp. 3185-3195, Jun 15 2013.

P. Melin and O. Castillo, "A review on the applications of type-2 fuzzy logic in classification and pattern recognition," Expert Systems with Applications, vol. 40, pp. 5413-5423, Oct 1 2013.

Y. Oysal and S. Yilmaz, "An adaptive wavelet network for function learning," Neural Computing & Applications, vol. 19, pp. 383-392, Apr 2010.

S. Yilmaz and Y. Oysal, "Fuzzy Wavelet Neural Network Models for Prediction and Identification of Dynamical Systems," IEEE Transactions on Neural Networks, vol. 21, pp. 1599-1609, Oct 2010.

Y. Oysal and S. Yilmaz, "An Adaptive Fuzzy Wavelet Network with Gradient Learning for Nonlinear Function Approximation," Journal of Intelligent Systems, vol. 23, pp. 201-2012, 2014.

S. Yilmaz, "Multilayer Dynamic Fuzzy Neural Network Design for Control and System Identification Applications," PhD PhD Thesis, Computer Engineering, Anadolu University, 2014.

R. H. Abiyev, "A Type-2 Fuzzy Wavelet Neural Network for Time Series Prediction," in IEA/AIE'10 Proceedings of the 23rd international conference on Industrial engineering and other applications of applied intelligent systems, 2010, pp. 518-527.

C. F. Juang, R. B. Huang, and Y. Y. Lin, "A Recurrent Self-Evolving Interval Type-2 Fuzzy Neural Network for Dynamic System Processing," IEEE Transactions on Fuzzy Systems, vol. 17, pp. 1092-1105, Oct 2009.

J. Nocedal and S. J. Wright, Numerical optimization, 2nd ed. New York: Springer, 2006.

M. J. L. Orr, "Introduction to Radial Basis Function Networks," C. f. C. S. U. o. Edinburgh, Ed., ed. Scotland, 1996.

J. Huhn and E. Hullermeier, "FURIA: an algorithm for unordered fuzzy rule induction," Data Mining and Knowledge Discovery, vol. 19, pp. 293-319, Dec 2009.

N. Friedman, D. Geiger, and M. Goldszmidt, "Bayesian network classifiers," Machine Learning, vol. 29, pp. 131-163, Nov-Dec 1997.

M. Kantardzic and MyiLibrary. (2011). Data mining concepts, models, methods, and algorithms (2nd ed.). Available: https://login.ezproxy1.lib.asu.edu/login?url=http://lib.myilibrary.com/detail.asp?id=323974

O. L. Mangasarian, W. N. Street, and W. H. Wolberg, "Breast-Cancer Diagnosis and Prognosis Via Linear-Programming," Operations Research, vol. 43, pp. 570-577, Jul-Aug 1995.

O. L. Mangasarian and W. H. Wolberg, "Cancer diagnosis via linear programming," SIAM News, vol. 23, pp. 1-18, 1990.