A variable precision grey-based multi-granulation rough set model and attribute reduction

Abstract Exploring rough set theory in the viewpoint of multi-granulation gradually attracts scholars attention in recent years. To handle uncertainty problems with grey information, in this paper, we devise a variable precision grey multi-granulation rough set (VPG-MGRS) by combining with grey system theory and multi-granulation rough set. We utilize the grey relational relation for further establishing multiple granular structures and then adopt a threshold to control the number of condition satisfied. After discussing several important properties of VPG-MGRS, we discover that the proposed VPG-MGRS model is a generalized classical MGRS. Meanwhile, we redefine the significance measures of attribute based on VPG-MGRS for attribute reduction. Last but not least, theoretical studies and numerical experiments have demonstrated that the VPG-MRGS-based attribute reduction algorithm is of feasibility and effectivity in handling uncertainty problems with grey information and provides a new technique for knowledge discovery, and the VPG-MGRS model enlarges the application fields of MGRS.

[1]  Deng Ju-Long,et al.  Control problems of grey systems , 1982 .

[2]  Chen Guo-hong,et al.  Rough grey sets , 2004 .

[3]  Jiye Liang,et al.  A fuzzy multigranulation decision-theoretic approach to multi-source fuzzy information systems , 2016, Knowl. Based Syst..

[4]  Suping Xu,et al.  The Models of Variable Precision Multigranulation Rough Sets , 2012, RSKT.

[5]  H. Hannah Inbarani,et al.  Optimistic Multi-granulation Rough Set Based Classification for Medical Diagnosis☆ , 2015 .

[6]  Jiye Liang,et al.  International Journal of Approximate Reasoning Multigranulation Decision-theoretic Rough Sets , 2022 .

[7]  Salvatore Greco,et al.  Fuzzy Similarity Relation as a Basis for Rough Approximations , 1998, Rough Sets and Current Trends in Computing.

[8]  Yi-Chung Hu,et al.  Tolerance rough sets for pattern classification using multiple grey single-layer perceptrons , 2016, Neurocomputing.

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

[10]  Xibei Yang,et al.  Variable Precision Multigranulation Rough Set and Attributes Reduction , 2014, Trans. Rough Sets.

[11]  Daniel Vanderpooten,et al.  A Generalized Definition of Rough Approximations Based on Similarity , 2000, IEEE Trans. Knowl. Data Eng..

[12]  Yiyu Yao,et al.  Rough set models in multigranulation spaces , 2016, Inf. Sci..

[13]  Weihua Xu,et al.  A Generalized Multi-granulation Rough Set Approach , 2011, ICIC.

[14]  Yuhua Qian,et al.  Multigranulation fuzzy rough set over two universes and its application to decision making , 2017, Knowl. Based Syst..

[15]  Tao Feng,et al.  Variable precision multigranulation decision-theoretic fuzzy rough sets , 2016, Knowl. Based Syst..

[16]  GuoDong Li,et al.  A grey-based rough approximation model for interval data processing , 2007, Inf. Sci..

[17]  Weihua Xu,et al.  Multi-granulation Fuzzy Rough Sets in a Fuzzy Tolerance Approximation Space , 2011 .

[18]  Jing-Yu Yang,et al.  Test cost sensitive multigranulation rough set: Model and minimal cost selection , 2013, Inf. Sci..

[19]  Jiye,et al.  Pessimistic Rough Decision , 2010 .

[20]  Jiye Liang,et al.  An information fusion approach by combining multigranulation rough sets and evidence theory , 2015, Inf. Sci..

[21]  Zhoujun Li,et al.  A novel variable precision (θ, σ)-fuzzy rough set model based on fuzzy granules , 2014, Fuzzy Sets Syst..

[22]  Xibei Yang,et al.  The Models of Dominance-Based Multigranulation Rough Sets , 2011, ICIC.

[23]  Ming Zhang,et al.  A Variable Muitlgranulation Rough Sets Approach , 2011, ICIC.

[24]  Z. Pawlak.  Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

[25]  Jing-Yu Yang,et al.  Dominance-based rough set approach and knowledge reductions in incomplete ordered information system , 2008, Inf. Sci..

[26]  Jiye Liang,et al.  Incomplete Multigranulation Rough Set , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[27]  Wei-Zhi Wu,et al.  Evidence-theory-based numerical characterization of multigranulation rough sets in incomplete information systems , 2016, Fuzzy Sets Syst..

[28]  Yi-Chung Hu,et al.  Pattern classification using grey tolerance rough sets , 2016, Kybernetes.

[29]  Didier Dubois,et al.  Putting Rough Sets and Fuzzy Sets Together , 1992, Intelligent Decision Support.

[30]  Jing-Yu Yang,et al.  Dominance-based rough set approach to incomplete interval-valued information system , 2009, Data Knowl. Eng..

[31]  Jiye Liang,et al.  Pessimistic rough set based decisions: A multigranulation fusion strategy , 2014, Inf. Sci..

[32]  Jiye Liang,et al.  International Journal of Approximate Reasoning an Efficient Rough Feature Selection Algorithm with a Multi-granulation View , 2022 .

[33]  Mustafa Mat Deris,et al.  Applying variable precision rough set model for clustering student suffering study's anxiety , 2012, Expert Syst. Appl..

[34]  Bao Qing Hu,et al.  Granular variable precision fuzzy rough sets with general fuzzy relations , 2015, Fuzzy Sets Syst..

[35]  Caihui Liu,et al.  On multi-granulation covering rough sets , 2014, Int. J. Approx. Reason..

[36]  Wei Wei,et al.  Variable precision multi-granulation rough set , 2012, 2012 IEEE International Conference on Granular Computing.

[37]  Jiye Liang,et al.  Local multigranulation decision-theoretic rough sets , 2017, Int. J. Approx. Reason..

[38]  Salvatore Greco,et al.  Rough approximation by dominance relations , 2002, Int. J. Intell. Syst..

[39]  Yanhong She,et al.  On the structure of the multigranulation rough set model , 2012, Knowl. Based Syst..

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

[41]  Shunxiang Wu,et al.  New and improved: grey multi-granulation rough sets , 2017, Int. J. Syst. Sci..

[42]  James Nga-Kwok Liu,et al.  A set covering based approach to find the reduct of variable precision rough set , 2014, Inf. Sci..

[43]  Jing-Yu Yang,et al.  Incomplete Multigranulation Rough Sets in Incomplete Ordered Decision System , 2011, ICIC.

[44]  Xiao Zhang,et al.  Multi-confidence rule acquisition and confidence-preserved attribute reduction in interval-valued decision systems , 2014, Int. J. Approx. Reason..

[45]  Shunxiang Wu,et al.  Different classes' ratio fuzzy rough set based robust feature selection , 2017, Knowl. Based Syst..

[46]  Yuhua Qian,et al.  NMGRS: Neighborhood-based multigranulation rough sets , 2012, Int. J. Approx. Reason..

[47]  Bing Huang,et al.  Intuitionistic fuzzy multigranulation rough sets , 2014, Inf. Sci..

[48]  Jing-Yu Yang,et al.  On multigranulation rough sets in incomplete information system , 2011, International Journal of Machine Learning and Cybernetics.

[49]  Xia Xiao,et al.  Three-way group decision making based on multigranulation fuzzy decision-theoretic rough set over two universes , 2017, Int. J. Approx. Reason..

[50]  Wu Shunxiang,et al.  Study of integrate models of rough sets and grey systems , 2005 .

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

[52]  J. Deng,et al.  Introduction to Grey system theory , 1989 .

[53]  Jianhua Dai,et al.  Rough set approach to incomplete numerical data , 2013, Inf. Sci..

[54]  Y. H. Qian,et al.  Rough Set Method Based on Multi-Granulations , 2006, 2006 5th IEEE International Conference on Cognitive Informatics.

[55]  Jinkun Chen,et al.  Feature selection via neighborhood multi-granulation fusion , 2014, Knowl. Based Syst..

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

[57]  Witold Pedrycz,et al.  Positive approximation: An accelerator for attribute reduction in rough set theory , 2010, Artif. Intell..

[58]  Caihui Liu,et al.  On Covering Multi-granulation Fuzzy Rough Sets , 2013 .

[59]  Lotfi A. Zadeh,et al.  Some reflections on soft computing, granular computing and their roles in the conception, design and utilization of information/intelligent systems , 1998, Soft Comput..