Interval Fuzzy Modeling Based on Minimizing-norm on Approximation Error

doi:10.16182/j.issn1004731x.joss.201803054

Abstract

Abstract: As the obtained data in many practical applications tend to be uncertain or inaccurate, conventional modeling methods characterized by deterministic model for this type of data have become undesirable. Taking linear programming and TS fuzzy model and some ideas from norm minimization into consideration, a novel method identifying interval fuzzy model (INFUMO) consisting of upper and lower TS fuzzy model (referred to as f_U and f_L) has been studied. In order to solve INFUMO, optimization problems based on minimizing-norm with respect to approximation error corresponding to f_U and f_L are constructed. Finally, optimization problems are solved by linear programming and INFUMO is thus constructed. The proposed method not only can deal with the problem that the conventional modeling method of uncertain data usually results in deterministic model, but also has better robustness.

Key words: norm on approximation error, INFUMO, linear programming, TS fuzzy model

CLC Number:

TP391.9

Liu Xiaoyong, Xiong Zhonggang, Yan Changguo. Interval Fuzzy Modeling Based on Minimizing-norm on Approximation Error[J]. Journal of System Simulation, 2018, 30(3): 1203-1209.

References 17

[1]	Fang S, Zhang Q, Ren W. An interval model updating strategy using interval response surface models[J]. Mechanical Systems and Signal Processing(S0888-3270), 2015, 60/61: 909-927.
[2]	Hao P.Interval regression analysis using support vector networks[J]. Fuzzy Sets and Systems(S0165-0114), 2009, 160(17): 2466-2485.
[3]	Wang C, Li J, Guo P.The normalized interval regression model with outlier detection and its real-world application to house pricing problems[J]. Fuzzy Sets and Systems (S0165-0114), 2015, 274: 109-123.
[4]	陶雪娇, 胡晓峰, 刘洋. 大数据研究综述[J]. 系统仿真学报, 2013, 25(增1): 142-146.TAO Xue-jiao, HU Xiao-feng, Liu Yang. Overview of Big Data Research [J]. Journal of System Simulation, 2013, 25(S1): 142-146.
[5]	宫夏屹, 李伯虎, 谷牧. 大数据平台技术综述[J]. 系统仿真学报, 2014, 26(3): 489-496.GONG Xia-yi, LI Bo-hu, GU Mu. Survey of Big Data Platform Technology [J]. Journal of System Simulation, 2014, 26(3): 489-496.
[6]	齐维贵, 张永明, 陈烈. 基于支持向量区间回归的供热负荷概率预报[J]. 吉林大学学报(工学版), 2010, 40(6): 1693-1697.QI Wei-gui, ZHANG Yong-ming, CHEN Lie. Probabilistic prediction approach of heat load based on support vector interval regression[J]. Journal of Jilin University(Engineering and Technology Edition), 2010, 40(6): 1693-1697.
[7]	李玲玲, 马东娟, 刘伯颖. 基于区间分析的非概率可靠性分析方法[J]. 机械强度, 2015, 37(1): 84-87.LI Ling-ling, MA Dong-juan, Liu Bai-yin. Non-probabilistic reliability method based on interval analysis[J]. Journal of Mechanical Strength, 2015, 37(1): 84-87.
[8]	王晓保, 岳继光, 杨臻明. 区间时间序列的混合预测模型[J]. 控制与决策, 2013, 28(12): 1915-1920.WANG Xiao-bao, YUE Ji-guang, YANG Zhen-ming. Hybrid model for interval-valued time series[J]. Control and Decesion, 2013, 28(12): 1915-1920.
[9]	吴铁军, 任世锦. 基于SVM的精确数-区间数回归模型建模方法[J]. 控制与决策, 2006, 21(12): 1326-1331.WU Tie-jun, REN Shi-jin. SVM Based Algorithm for Regressive Modeling with Accurate Data Input-interval Number Output[J]. Control and Decesion, 2006, 21(12), 1326-1331.
[10]	Tanaka H, Lee H.Fuzzy linear regression combining central tendency and possibilistic properties[C]// Proceedings of the Sixth IEEE International Conference onFuzzy Systems, 1997: 63-68.
[11]	Hong D H, Hwang C.Interval regression analysis using quadratic loss support vector machine[J]. Fuzzy Systems, IEEE Transactions on (S1063-6706), 2005, 13(2): 229-237.
[12]	Lee H, Tanaka H.Upper and lower approximation models in interval regression using regression quantile techniques[J]. European Journal of Operational Research(S0377-2217), 1999, 116(3): 653-666.
[13]	Huang L, Zhang B, Huang Q.Robust interval regression analysis using neural networks[J]. Fuzzy sets and systems(S0165-0114), 1998, 97(3): 337-347.
[14]	Skrjanc I, Blazic S, Agamennoni O E.Identification of dynamical systems with a robust interval fuzzy model[J]. Automatica(S0005-1098), 2005, 41(2): 327-332.
[15]	Skrjanc I, Blazic S, Agamennoni O.Interval Fuzzy Model Identification Using L-infinity Norm[J]. Fuzzy Systems, IEEE Transactions on(S1063-6706), 2005, 13(5): 561-568.
[16]	Skrjanc I, Blazic S, Agamennoni O E.Interval fuzzy modeling applied to Wiener models with uncertainties[J]. Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on(S1083-4427), 2005, 35(5): 1092-1095.
[17]	Takagi T, Sugeno M.Fuzzy identification of systems and its applications to modeling and control[J]. Systems, Man and Cybernetics, IEEE Transactions on (S1083-4427), 1985, 15(1): 116-132.