Document Type : Research Paper


1 Center of Computing, Xinyang Normal University, Xinyang 464000, P. R. China

2 School of Computer and Information Technology, Xinyang Normal University, Xinyang 464000, P. R. China


Representation of a granule, relation and operation between two granules are mainly researched in granular computing. Hyperbox granular computing classification algorithms (HBGrC) are proposed based on interval analysis. Firstly, a granule is represented as the hyperbox which is the Cartesian product of $N$ intervals for classification in the $N$-dimensional space. Secondly, the relation between two hyperbox granules is measured by the novel positive valuation function induced by the two endpoints of an interval, where the operations between two hyperbox granules are designed so as to include granules with different granularity. Thirdly, hyperbox granular computing classification algorithms are designed on the basis of the operations between two hyperbox granules, the fuzzy inclusion relation between two hyperbox granules, and the granularity threshold. We demonstrate the superior performance of the proposed algorithms compared with the traditional classification algorithms, such as, Random Forest (RF), Support Vector Machines (SVMs), and Multilayer Perceptron (MLP).


[1] H. M. Barakat, M. E. El-Adll and A. E. Alyb, Prediction intervals of future observations for
a sample of random size from any continuous distribution, Mathematics and Computers in
Simulation, 97 (2014), 1-13.
[2] G. Bortolan and W. Pedrycz, Hyperbox classifiers for arrhythmia classification, Kybernetes,
36(3-4) (2007), 531-547.
[3] Y. Chen, Q. Zhu, K.Wu, S. Zhu and Z. Zeng, A binary granule representation for uncertainty
measures in rough set theory, Journal of Intelligent and Fuzzy Systems, 28(2) (2015), 867-
[4] C. Cortes and V. Vapnik, Support-vector networks, Machine Learning, 20(3) (1995), 273-297.
[5] Z. Fu, K. Ren, J. Shu, X. Sun and F. Huang, Enabling personalized search over encrypted
outsourced data with efficiency improvement, IEEE Transactions on Parallel and Distributed
Systems, 27(9) (2016), 2546-2559.
[6] Z. Fu, X. Sun, N. Linge and L. Zhou, Achieving effective cloud search services: multi-keyword
ranked search over encrypted cloud data supporting synonym query, IEEE Transactions on
Consumer Electronics, 60(1) (2014), 164-172.
[7] T. K. Ho, The random subspace method for constructing decision forests, IEEE Transactions
on Pattern Analysis and Machine Intelligence, 20(8) (1998), 832-844.
[8] P. Honko, Association discovery from relational data via granular computing, Information
Sciences, 234 (2013), 136-149.
[9] X. Hu, W. Pedrycz and X. Wang, Comparative analysis of logic operators: A perspective of
statistical testing and granular computing, International Journal of Approximate Reasoning,
66 (2015), 73-90.
[10] V. G. Kaburlasos and A. Kehagias, Fuzzy Inference System (FIS) extensions based on the
lattice theory, IEEE Transactions on Fuzzy Systems, 22(3) (2014),531-546.
[11] V. G. Kaburlasos and T. P. Pachidis, A Lattice-Computing ensemble for reasoning based on
formal fusion of disparate data types, and an industrial dispensing application, Information
Fusion, 16 (2014), 68-83.
[12] V. G. Kaburlasos, S. E. Papadakis and G. A. Papakostas, Lattice computing extension of the
FAM Neural classifier for human facial expression recognition, IEEE Transactions on Neural
Networks and Learning Systems, 24(10) (2013), 1526-1538.
[13] V. G. Kaburlasos and G. A. Papakostas, Learning distributions of image features by interactive
fuzzy lattice reasoning in pattern recognition applications, IEEE Computational
Intelligence Magazine, 10(3) (2015), 42-51.
[14] J. Kerr-Wilson and W. Pedrycz, Design of rule-based models through information granulation,
Expert System with Applications, 46 (2016),274-285.
[15] A. Khalid and I. Beg, Incomplete interval valued fuzzy preference relations, Information
Sciences, 348 (2016), 15-24.
[16] L. Maciura and J. G. Bazan, Granular computing in mosaicing of images from capsule
endoscopy, Natural Computing, 14(4) (2015), 569-577.
[17] R. E. Moore, R. B. Kearfott and M. J. Cloud, Introduction to Interval Analysis, SIAM Press,
Philadelphia, 2009.
[18] K. R. Opara and O. Hryniewicz, Computation of general correlation coefficients for interval
data, International Journal of Approximate Reasoning, 73 (2016), 56-75.
[19] W. Pedrycz, Granular fuzzy rule-based architectures: Pursuing analysis and design in the
framework of granular computing, Intelligent Decision Technologies, 9(4) (2015), 321-330.
[20] V. Petridis and V. G. Kaburlasos, Fuzzy lattice neural network (FLNN): a hybrid model for
learning, IEEE Transactions on Neural Networks, 9(5) (1998), 877-890.
[21] V. Petridis and V. G. Kaburlasos, Learning in the framework of fuzzy lattices, IEEE Transactions
on Fuzzy Systems, 7(4) (1999), 422-440.
[22] B. Ploj, Advances in Machine Learning Research, Nova Press, New York, 2014.
[23] J. Pyrzowski, M. Siemiski, A. Sarnowska, J. Jedrzejczak and W. M. Nyka, Interval analysis of
interictal EEG: pathology of the alpha rhythm in focal epilepsy, Scientific Reports 5, 16230
(2015), 1-10.
[24] B. D. Ripley, Pattern Recognition and Neural Networks, Cambridge University Press, Cambridge,
[25] M. Ristin, M. Guillaumin, J. Gall and L. V. Gool, Incremental learning of random forests
for large-scale image classification, IEEE Transactions on Pattern Analysis and Machine
Intelligence, 38(3) (2016), 490-503.
[26] A. V. Savchenko, Fast multi-class recognition of piecewise regular objects based on sequential
three-way decisions and granular computing, Knowledge-Based Systems, 91 (2016), 252-262.
[27] H. Sossa and E. Guevara, Efficient training for dendrite morphological neural networks,
Neurocomputing, 131 (2014), 132-142.
[28] S. Suriadi, C. Ouyang, W. M. P. van der Aalst and A. H. M. ter Hofstede, Event interval
analysis: Why do processes take time? Decision Support Systems, 79 (2015), 77-98.
[29] Y. Yao and Y. She, Rough set models in multigranulation spaces, Information Sciences, 327
[30] Y. Y. Yao and L. Q. Zhao, A measurement theory view on the granularity of partitions,
Information Sciences, 213 (2012), 1-13.
[31] L. A. Zadeh, Some reflections on soft computing, granular computing and their roles in the
conception, design and utilization of information/intelligent systems, Soft Computing, 2(1)
(1998), 23-25.