Three-way decisions model based on tolerance rough fuzzy set

Based on Bayesian decision theory, three-way decisions model (TWDM) proposed by Yao gives new semantic interpretations of positive region, negative region and boundary region. Some extensions of TWDM have been proposed by different authors and have been successfully applied to many fields, such as soft computing, data mining and decision making. However existing three-way decisions models are almost developed in certainty environment, which limits their applications in uncertainty environment. In order to deal with this problem, based on tolerance rough fuzzy set, a TWDM is proposed in this paper. The main contributions of this paper include two aspects: (1) the tolerance rough fuzzy set which is extended from rough fuzzy set is introduced, and some basic properties of the tolerance rough fuzzy set are investigated. (2) The TWDM with respect to the tolerance rough fuzzy set is proposed. In addition, an example is given to illustrate the computation processes of the TWDM.

[1]  Hai-Long Yang,et al.  Multigranulation decision-theoretic rough sets in incomplete information systems , 2015, Int. J. Mach. Learn. Cybern..

[2]  L. Kuncheva.  Fuzzy rough sets: application to feature selection , 1992 .

[3]  Yu-Lin He,et al.  Fuzziness based semi-supervised learning approach for intrusion detection system , 2017, Inf. Sci..

[4]  Bing Huang,et al.  Sequential three-way decision and granulation for cost-sensitive face recognition , 2016, Knowl. Based Syst..

[5]  Yan Chen,et al.  An adjustable multigranulation fuzzy rough set , 2016, Int. J. Mach. Learn. Cybern..

[6]  Ebrahim Farjah,et al.  Application of core vector machines for induction motor drive fault diagnosis , 2015, J. Intell. Fuzzy Syst..

[7]  Bing Shi,et al.  Regression-based three-way recommendation , 2017, Inf. Sci..

[8]  Rong Yang,et al.  Classification based on Choquet integral , 2014, J. Intell. Fuzzy Syst..

[9]  Huanhuan Chen,et al.  Robust twin boosting for feature selection from high-dimensional omics data with label noise , 2015, Inf. Sci..

[10]  Joshua Zhexue Huang,et al.  Recent advances in multiple criteria decision making techniques , 2016, Int. J. Mach. Learn. Cybern..

[11]  Wei-Zhi Wu,et al.  Decision-theoretic rough set: A multicost strategy , 2016, Knowl. Based Syst..

[12]  Yiyu Yao,et al.  Probabilistic approaches to rough sets , 2003, Expert Syst. J. Knowl. Eng..

[13]  Yiyu Yao,et al.  A Decision Theoretic Framework for Approximating Concepts , 1992, Int. J. Man Mach. Stud..

[14]  Yiyu Yao.  Combination of Rough and Fuzzy Sets Based on α-Level Sets , 1997 .

[15]  Qiwei Gu,et al.  Consistent feature selection and its application to face recognition , 2014, Journal of Intelligent Information Systems.

[16]  Salvatore Greco,et al.  Rough approximation of a preference relation by dominance relations , 1999, Eur. J. Oper. Res..

[17]  Yu-lin He,et al.  OWA operator based link prediction ensemble for social network , 2015, Expert Syst. Appl..

[18]  Hong Chen,et al.  RFRR: Robust Fuzzy Rough Reduction , 2013, IEEE Transactions on Fuzzy Systems.

[19]  Yu-Lin He,et al.  Fuzzy nonlinear regression analysis using a random weight network , 2016, Inf. Sci..

[20]  Weihua Xu,et al.  Double-quantitative decision-theoretic rough set , 2015, Inf. Sci..

[21]  Yumin Chen,et al.  Three-way decision reduction in neighborhood systems , 2016, Appl. Soft Comput..

[22]  Yiyu Yao,et al.  Three-way decisions with probabilistic rough sets , 2010, Inf. Sci..

[23]  Qing Li,et al.  Three-way decisions based software defect prediction , 2016, Knowl. Based Syst..

[24]  Jiye Liang,et al.  Hesitant fuzzy linguistic rough set over two universes model and its applications , 2018, Int. J. Mach. Learn. Cybern..

[25]  Rong Yang,et al.  Cross-oriented choquet integrals and their applications on data classification , 2015, J. Intell. Fuzzy Syst..

[26]  Decui Liang,et al.  Deriving three-way decisions from intuitionistic fuzzy decision-theoretic rough sets , 2015, Inf. Sci..

[27]  Zengtai Gong,et al.  The further investigation of variable precision intuitionistic fuzzy rough set model , 2017, Int. J. Mach. Learn. Cybern..

[28]  Bao Qing Hu,et al.  Three-way decision spaces based on partially ordered sets and three-way decisions based on hesitant fuzzy sets , 2016, Knowl. Based Syst..

[29]  Decui Liang,et al.  A novel three-way decision model based on incomplete information system , 2016, Knowl. Based Syst..

[30]  Witold Pedrycz,et al.  A Study on Relationship Between Generalization Abilities and Fuzziness of Base Classifiers in Ensemble Learning , 2015, IEEE Transactions on Fuzzy Systems.

[31]  Andrzej Skowron,et al.  Tolerance Approximation Spaces , 1996, Fundam. Informaticae.

[32]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[33]  Yiyu Yao,et al.  Generalization of Rough Sets using Modal Logics , 1996, Intell. Autom. Soft Comput..

[34]  Shengli Zhang,et al.  The Decision Delay in Finite-Length MMSE–DFE Systems , 2015, Wirel. Pers. Commun..

[35]  James F. Peters,et al.  Proximal three-way decisions: Theory and applications in social networks , 2016, Knowl. Based Syst..

[36]  Yuhua Qian,et al.  Three-way cognitive concept learning via multi-granularity , 2017, Inf. Sci..

[37]  Wojciech Ziarko,et al.  Variable Precision Rough Set Model , 1993, J. Comput. Syst. Sci..

[38]  Xizhao Wang,et al.  Fuzziness based sample categorization for classifier performance improvement , 2015, J. Intell. Fuzzy Syst..

[39]  Bao Qing Hu,et al.  Three-way decisions space and three-way decisions , 2014, Inf. Sci..

[40]  Decui Liang,et al.  Three-way group decisions with decision-theoretic rough sets , 2016, Inf. Sci..

[41]  Yiyu Yao,et al.  Interval sets and three-way concept analysis in incomplete contexts , 2016, International Journal of Machine Learning and Cybernetics.

[42]  Weixin Xie,et al.  Extending twin support vector machine classifier for multi-category classification problems , 2013, Intell. Data Anal..

[43]  Yiyu Yao,et al.  Advances in three-way decisions and granular computing , 2016, Knowl. Based Syst..

[44]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[45]  Xiaoyong Du,et al.  A Novel Approach to Building a Robust Fuzzy Rough Classifier , 2015, IEEE Transactions on Fuzzy Systems.

[46]  Bao Qing Hu,et al.  Fuzzy probabilistic rough sets and their corresponding three-way decisions , 2016, Knowl. Based Syst..

[47]  Zhen Ji,et al.  Towards a Memetic Feature Selection Paradigm [Application Notes] , 2010, IEEE Computational Intelligence Magazine.

[48]  S. Nanda,et al.  Fuzzy rough sets , 1992 .

[49]  Xizhao Wang,et al.  Building a Rule-Based Classifier—A Fuzzy-Rough Set Approach , 2010, IEEE Transactions on Knowledge and Data Engineering.

[50]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[51]  Xizhao Wang,et al.  Learning from big data with uncertainty - editorial , 2015, J. Intell. Fuzzy Syst..