Probabilistic fuzzy rough sets

We extend the fuzzy rough set as probabilistic fuzzy rough set (PFRS) on a fuzzy probabilistic approximation space. The proposed PFRS models both vague and uncertain information at the same time. The viability of PFRS in decision making is illustrated through a case study. PFRS is shown to be useful for both probabilistic as well as deterministic problems.

[1]  Qinghua Hu,et al.  Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation , 2007, Pattern Recognit..

[2]  Yiyu Yao,et al.  Probabilistic rough set approximations , 2008, Int. J. Approx. Reason..

[3]  Xizhao Wang,et al.  On the generalization of fuzzy rough sets , 2005, IEEE Transactions on Fuzzy Systems.

[4]  Yiyu Yao,et al.  Decision-Theoretic Rough Set Models , 2007, RSKT.

[5]  Pawan Lingras,et al.  Survey of Rough and Fuzzy Hybridization , 2007, 2007 IEEE International Fuzzy Systems Conference.

[6]  Qiang Shen,et al.  New Approaches to Fuzzy-Rough Feature Selection , 2009, IEEE Transactions on Fuzzy Systems.

[7]  Slavka Bodjanova,et al.  Approximation of fuzzy concepts in decision making , 1997, Fuzzy Sets Syst..

[8]  Tong-Jun Li,et al.  An axiomatic characterization of probabilistic rough sets , 2014, Int. J. Approx. Reason..

[9]  Qiang Shen,et al.  Semantics-preserving dimensionality reduction: rough and fuzzy-rough-based approaches , 2004, IEEE Transactions on Knowledge and Data Engineering.

[10]  Jiye Liang,et al.  Inclusion degree: a perspective on measures for rough set data analysis , 2002, Inf. Sci..

[11]  Yiyu Yao,et al.  Attribute reduction in decision-theoretic rough set models , 2008, Inf. Sci..

[12]  Chris Cornelis,et al.  Fuzzy Rough Sets: The Forgotten Step , 2007, IEEE Transactions on Fuzzy Systems.

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

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

[15]  Qiang Shen,et al.  Centre for Intelligent Systems and Their Applications Fuzzy Rough Attribute Reduction with Application to Web Categorization Fuzzy Rough Attribute Reduction with Application to Web Categorization Fuzzy Sets and Systems ( ) – Fuzzy–rough Attribute Reduction with Application to Web Categorization , 2022 .

[16]  Jiang Hua.  Study on the Application of Rough Sets Theory in Machine Learning , 2008, 2008 Second International Symposium on Intelligent Information Technology Application.

[17]  Anna Maria Radzikowska,et al.  A comparative study of fuzzy rough sets , 2002, Fuzzy Sets Syst..

[18]  Dun Liu,et al.  Incremental updating approximations in probabilistic rough sets under the variation of attributes , 2015, Knowl. Based Syst..

[19]  Andrzej Skowron,et al.  Rough mereology: A new paradigm for approximate reasoning , 1996, Int. J. Approx. Reason..

[20]  Degang Chen,et al.  The Model of Fuzzy Variable Precision Rough Sets , 2009, IEEE Transactions on Fuzzy Systems.

[21]  Wojciech Ziarko,et al.  Probabilistic approach to rough sets , 2008, Int. J. Approx. Reason..

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

[23]  Nehad N. Morsi,et al.  Axiomatics for fuzzy rough sets , 1998, Fuzzy Sets Syst..

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

[25]  Zheng Pei,et al.  On the topological properties of fuzzy rough sets , 2005, Fuzzy Sets Syst..

[26]  Didier Dubois,et al.  Formal Representations of Uncertainty , 2010, Decision-making Process.

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

[28]  Dominik Slezak,et al.  The investigation of the Bayesian rough set model , 2005, Int. J. Approx. Reason..

[29]  Alicja Mieszkowicz-Rolka,et al.  Variable Precision Fuzzy Rough Sets , 2004, Trans. Rough Sets.

[30]  Yi-Fan Wang,et al.  Mining stock price using fuzzy rough set system , 2003, Expert Syst. Appl..

[31]  Guoyin Wang,et al.  Monotonic uncertainty measures for attribute reduction in probabilistic rough set model , 2015, Int. J. Approx. Reason..

[32]  Andrzej Skowron,et al.  Rough Mereological Foundatins for Design, Analysis, Synthesis, and Control in Distributed Systems , 1998, Inf. Sci..

[33]  Qinghua Hu,et al.  Information-preserving hybrid data reduction based on fuzzy-rough techniques , 2006, Pattern Recognit. Lett..

[34]  Wen-Xiu Zhang,et al.  Theory of including degrees and its applications to uncertainty inferences , 1996, Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium.

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

[36]  Qiang Shen,et al.  Fuzzy-Rough Sets Assisted Attribute Selection , 2007, IEEE Transactions on Fuzzy Systems.

[37]  Theresa Beaubouef,et al.  Information-Theoretic Measures of Uncertainty for Rough Sets and Rough Relational Databases , 1998, Inf. Sci..

[38]  Salvatore Greco,et al.  Rough Membership and Bayesian Confirmation Measures for Parameterized Rough Sets , 2005, RSFDGrC.

[39]  Chengdong Shi.  The Application of Rough Sets and Fuzzy Sets in the Supply Chain Knowledge Sharing Risk Early-Warning , 2009, 2009 Sixth International Conference on Fuzzy Systems and Knowledge Discovery.

[40]  Yiyu Yao,et al.  Quantitative rough sets based on subsethood measures , 2014, Inf. Sci..

[41]  L. Zadeh.  Probability measures of Fuzzy events , 1968 .

[42]  Wen-Xiu Zhang,et al.  Hybrid monotonic inclusion measure and its use in measuring similarity and distance between fuzzy sets , 2009, Fuzzy Sets Syst..

[43]  Pawan Lingras,et al.  Fuzzy-rough and rough-fuzzy serial combinations in neurocomputing , 2001, Neurocomputing.

[44]  Salvatore Greco,et al.  Assessing the Quality of Rules with a New Monotonic Interestingness Measure Z , 2006, ICAISC.

[45]  Donald H. Kraft,et al.  Vocabulary mining for information retrieval: rough sets and fuzzy sets , 2001, Inf. Process. Manag..

[46]  Manish Sarkar.  Measures of ruggedness using fuzzy-rough sets and fractals: applications in medical time series , 2001, 2001 IEEE International Conference on Systems, Man and Cybernetics. e-Systems and e-Man for Cybernetics in Cyberspace (Cat.No.01CH37236).

[47]  Sankar K. Pal,et al.  Case generation using rough sets with fuzzy representation , 2004, IEEE Transactions on Knowledge and Data Engineering.

[48]  Mei Zhang,et al.  A rough set approach to knowledge reduction based on inclusion degree and evidence reasoning theory , 2003, Expert Syst. J. Knowl. Eng..

[49]  Qiang Shen,et al.  Fuzzy-rough data reduction with ant colony optimization , 2005, Fuzzy Sets Syst..

[50]  Qun-Feng Zhang,et al.  On the application of rough sets to data mining in economic practice , 2009, 2009 International Conference on Machine Learning and Cybernetics.

[51]  Desire L. Massart,et al.  Rough sets theory , 1999 .