# American Institute of Mathematical Sciences

• Previous Article
Comments on ''Generalized support set invariancy sensitivity analysis in linear optimization''
• JIMO Home
• This Issue
• Next Article
Global convergence of modified Polak-Ribière-Polyak conjugate gradient methods with sufficient descent property
July  2008, 4(3): 581-609. doi: 10.3934/jimo.2008.4.581

## The framework of axiomatics fuzzy sets based fuzzy classifiers

 1 Research Center of Information and Control, Dalian University of Technology, Dalian, 116024, China 2 Dept. of Computing, Curtin University of Technology, Bentley, WA, 6102, Australia

Received  November 2006 Revised  March 2008 Published  July 2008

In this paper we will propose a new classifier design based on the AFS fuzzy theory. First, we will briefly review the current researches in data classification based on fuzzy and rough set theories and then present the AFS framework. Second, we will present new membership functions for fuzzy sets with their logic operations in the AFS framework and then tackle some theoretical and computational problems related to classifier design. Third, we will develop a new approach for fuzzy classifier design based on the proposed membership functions and their logic operations. Finally, a well-known example is used to illustrate its effectiveness. The advantage of this classifier is in two-folds. One is that it can mimic the human reasoning comprehensively and offers a far more flexible and effective way for the study of large-scale intelligent systems. The other is its simplicity in methodology and mathematical beauty in fuzzy theory.
Citation: Xiaodong Liu, Wanquan Liu. The framework of axiomatics fuzzy sets based fuzzy classifiers. Journal of Industrial and Management Optimization, 2008, 4 (3) : 581-609. doi: 10.3934/jimo.2008.4.581
 [1] Lina Zhang, Li Ma, Shan Chen. Design of the integrated AFS and DYC scheme for vehicles via FTSM and SOSM techniques. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022077 [2] Muhammad Aamer Rashid, Sarfraz Ahmad, Muhammad Kamran Siddiqui, Juan L. G. Guirao, Najma Abdul Rehman. Topological indices of discrete molecular structure. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2487-2495. doi: 10.3934/dcdss.2020418 [3] Zhen Ming Ma, Ze Shui Xu, Wei Yang. Approach to the consistency and consensus of Pythagorean fuzzy preference relations based on their partial orders in group decision making. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2615-2638. doi: 10.3934/jimo.2020086 [4] Wenjuan Jia, Yingjie Deng, Chenyang Xin, Xiaodong Liu, Witold Pedrycz. A classification algorithm with Linear Discriminant Analysis and Axiomatic Fuzzy Sets. Mathematical Foundations of Computing, 2019, 2 (1) : 73-81. doi: 10.3934/mfc.2019006 [5] Abdel-Rahman Hedar, Ahmed Fouad Ali, Taysir Hassan Abdel-Hamid. Genetic algorithm and Tabu search based methods for molecular 3D-structure prediction. Numerical Algebra, Control and Optimization, 2011, 1 (1) : 191-209. doi: 10.3934/naco.2011.1.191 [6] Lin Lu, Qi Wang, Yongzhong Song, Yushun Wang. Local structure-preserving algorithms for the molecular beam epitaxy model with slope selection. Discrete and Continuous Dynamical Systems - B, 2021, 26 (9) : 4745-4765. doi: 10.3934/dcdsb.2020311 [7] Jun Xie, Jinlong Yuan, Dongxia Wang, Weili Liu, Chongyang Liu. Uniqueness of solutions to fuzzy relational equations regarding Max-av composition and strong regularity of the matrices in Max-av algebra. Journal of Industrial and Management Optimization, 2018, 14 (3) : 1007-1022. doi: 10.3934/jimo.2017087 [8] Christoforidou Amalia, Christian-Oliver Ewald. A lattice method for option evaluation with regime-switching asset correlation structure. Journal of Industrial and Management Optimization, 2021, 17 (4) : 1729-1752. doi: 10.3934/jimo.2020042 [9] Pablo Neme, Jorge Oviedo. A note on the lattice structure for matching markets via linear programming. Journal of Dynamics and Games, 2021, 8 (1) : 61-67. doi: 10.3934/jdg.2021001 [10] Guangmei Shao, Wei Xue, Gaohang Yu, Xiao Zheng. Improved SVRG for finite sum structure optimization with application to binary classification. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2253-2266. doi: 10.3934/jimo.2019052 [11] Wenjun Liu, Yukun Xiao, Xiaoqing Yue. Classification of finite irreducible conformal modules over Lie conformal algebra $\mathcal{W}(a, b, r)$. Electronic Research Archive, 2021, 29 (3) : 2445-2456. doi: 10.3934/era.2020123 [12] Cui-Ping Cheng, Wan-Tong Li, Zhi-Cheng Wang. Asymptotic stability of traveling wavefronts in a delayed population model with stage structure on a two-dimensional spatial lattice. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 559-575. doi: 10.3934/dcdsb.2010.13.559 [13] Pavel Eichler, Radek Fučík, Robert Straka. Computational study of immersed boundary - lattice Boltzmann method for fluid-structure interaction. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 819-833. doi: 10.3934/dcdss.2020349 [14] D. Warren, K Najarian. Learning theory applied to Sigmoid network classification of protein biological function using primary protein structure. Conference Publications, 2003, 2003 (Special) : 898-904. doi: 10.3934/proc.2003.2003.898 [15] Robert I. McLachlan, Ander Murua. The Lie algebra of classical mechanics. Journal of Computational Dynamics, 2019, 6 (2) : 345-360. doi: 10.3934/jcd.2019017 [16] Richard H. Cushman, Jędrzej Śniatycki. On Lie algebra actions. Discrete and Continuous Dynamical Systems - S, 2020, 13 (4) : 1115-1129. doi: 10.3934/dcdss.2020066 [17] Paul Breiding, Türkü Özlüm Çelik, Timothy Duff, Alexander Heaton, Aida Maraj, Anna-Laura Sattelberger, Lorenzo Venturello, Oǧuzhan Yürük. Nonlinear algebra and applications. Numerical Algebra, Control and Optimization, 2021  doi: 10.3934/naco.2021045 [18] Uta Renata Freiberg. Einstein relation on fractal objects. Discrete and Continuous Dynamical Systems - B, 2012, 17 (2) : 509-525. doi: 10.3934/dcdsb.2012.17.509 [19] David Bechara Senior, Umberto L. Hryniewicz, Pedro A. S. Salomão. On the relation between action and linking. Journal of Modern Dynamics, 2021, 17: 319-336. doi: 10.3934/jmd.2021011 [20] Neşet Deniz Turgay. On the mod p Steenrod algebra and the Leibniz-Hopf algebra. Electronic Research Archive, 2020, 28 (2) : 951-959. doi: 10.3934/era.2020050

2021 Impact Factor: 1.411