Hyperbox Granular Computing Classifiers Based on Fuzzy Lattices
LIU Hong-Bing1, 2, WU Chang-An1, XIONG Sheng-Wu2
1. School of Computer and Information Technology, Xinyang Normal University, Xinyang 464000
2. School of Computer Science and Technology, Wuhan University of Technology, Wuhan 430070
Representation, relation and operation of granules are the main research content of granular computing. A hyperbox granule is represented by a vector including a beginning point and an end point. The inconsistency between the partial ordering relation in vector space and the partial ordering relation in hyperbox granule space is analyzed and then eliminated by the order-preserving function. The fuzzy inclusion relation between two hyperbox granules is formed by nonlinear positive valuation function and the order-preserving function between the lattice and its dual lattice. The join operator and decomposition operator between two granules are designed to achieve the granules with different granularity. The algebraic system which is composed of hyperbox granule set, fuzzy inclusion relation and the operators between two granules is proved as fuzzy lattice. Hyperbox granular computing classifiers are formed based on fuzzy lattice, and verified by classification problems on machine learning dataset. The experimental results show that hyperbox granular computing classifiers have a generalization ability comparable to that of fuzzy lattice reasoning classifiers with less number of hyperbox granules.
[1] Skowron A, Stepaniuk J. Information Granular: Towards Foundation of Granular Computing. International Journal of Intelligent System, 2001, 16(1): 57-85
[2] Yao Yiyu. Granular Computing: Past, Present and Future // Proc of the IEEE International Conference on Granular Computing. Hangzhou, China, 2008: 80-85
[3] Yao Yiyu. Interpreting Concept Learning in Cognitive Informatics and Granular Computing. IEEE Trans on Systems, Man and Cybernetics, 2009, 39(4): 855-866
[4] Zhang Ling, Zhang Bo. Theory and Applications of Problem Solving. 2nd Edition. Beijing, China: Tsinghua University Press, 2007 (in Chinese)
(张 铃,张 钹.问题求解的理论及应用.第2版.北京:清华大学出版社, 2007)
[5] Lin T Y. Granular Computing on Binary Relations II:Rough Set Representations and Belief Functions[EB/OL].[2012-10-01]. http: // xanada.cs.sj-su.edu /~tylin/classes / cs267_old / final / id3 / MyPaperWithmyConclusion.pdf
[6] Zhang Ling, Zhang Bo. Fuzzy Tolerance Quotient Spaces and Fuzzy Subsets. Science China: Series F, 2011, 41(1): 1-11(in Chinese)
(张 铃,张 钹.模糊相容商空间与模糊子集.中国科学:F辑, 2011, 41(1): 1-11)
[7] Zadeh L A. Towards a Theory of Fuzzy Information Granulation and Its Centrality in Human Reasoning and Fuzzy Logic. Fuzzy Sets and Systems, 1997, 90 (2): 111-127
[8] Graa M. A Brief Review of Lattice Computing // Proc of the IEEE World Congress on Computational Intelligence. Hong Kong, China, 2008: 1777-1781
[9] Graa M, Villaverde I, Maldonado J O, et al. Two Lattice Computing Approaches for the Unsupervised Segmentation of Hyperspectral Images. Neurocomputing, 2009, 72(10/11/12): 2111-2120
[10] Nanda S. Fuzzy Lattices. Bulletin of the Calcutta Mathematical Society, 1989, 81(1): 1-2
[11] Kaburlasos V G, Papadakis S E. Granular Self-Organizing Map (gr-SOM) for Structure Identification. Neural Networks, 2006, 19(5): 623-643
[12] Kaburlasos V G, Athanasiadis I N, Mitkas P A. Fuzzy Lattice Reasoning (FLR) Classifier and Its Application for Ambient Ozone Estimation. International Journal of Approximate Reasoning, 2007, 45(1): 152-188
[13] Miao Duoqian, Fan Shidong. The Calculation of Knowledge Granulation and Its Application. Systems Engineering-Theory and Practice, 2002, 22(1): 48-56 (in Chinese)
(苗夺谦,范世栋.知识的粒度计算及其应用.系统工程理论与实践, 2002, 22(1): 48-56)
[14] Lang K J, Witbrock D J. Learning to Tell Two Spirals Apart // Touretzky D, Hinton G, Sejnowcki T, eds. Proc of the Connectionist Models Summer School. San Mateo, USA: Morgan Kaufmann, 1988: 52-59
2013, Vol. 26 
