Rough sets in the Soft Computing environment

Problem-solving in situations of uncertainty is a key issue in achieving effective computational systems. Various techniques have been developed to address uncertainty, including Soft Computing, which has established itself as an area of significant interest. On the other hand, rough sets theory has become an effective means of dealing with uncertainty, particularly when it arises as a result of inconsistencies in the data. The present paper surveys an analysis of the relationship between rough sets and other components of Soft Computing, and of how this hybridization helps improve system performance.

[1]  Ray R. Hashemi,et al.  A hybrid intelligent system for predicting bank holding structures , 1998, Eur. J. Oper. Res..

[2]  Emile Fiesler,et al.  High-order and multilayer perceptron initialization , 1997, IEEE Trans. Neural Networks.

[3]  Jing-Ping Jiang,et al.  The integrated methodology of rough sets theory, fuzzy logic and genetic algorithms for multisensor fusion , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

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

[5]  James L. McClelland,et al.  Explorations in parallel distributed processing: a handbook of models, programs, and exercises , 1988 .

[6]  Wojciech Ziarko,et al.  Acquisition of hierarchy‐structured probabilistic decision tables and rules from data , 2003, Expert Syst. J. Knowl. Eng..

[7]  Yiyu Yao,et al.  Interpretation of Belief Functions in The Theory of Rough Sets , 1998, Inf. Sci..

[8]  Qunxiong Zhu,et al.  Rough set-based heuristic hybrid recognizer and its application in fault diagnosis , 2009, Expert Syst. Appl..

[9]  Gianpiero Cattaneo,et al.  Entropies and Co-Entropies of Coverings with Application to Incomplete Information Systems , 2007, Fundam. Informaticae.

[10]  Jerzy W. Grzymala-Busse,et al.  Rough sets : New horizons in commercial and industrial AI , 1995 .

[11]  Francisco Herrera,et al.  Enhancing evolutionary instance selection algorithms by means of fuzzy rough set based feature selection , 2012, Inf. Sci..

[12]  Xiangyang Wang,et al.  Feature selection based on rough sets and particle swarm optimization , 2007, Pattern Recognit. Lett..

[13]  Tansel Özyer,et al.  Utilizing Rough Sets and Multi-objective Genetic Algorithms for Automated Clustering , 2004, Rough Sets and Current Trends in Computing.

[14]  Chris Cornelis,et al.  Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge , 2003 .

[15]  Huaguang Zhang,et al.  Two new operators in rough set theory with applications to fuzzy sets , 2004, Inf. Sci..

[16]  Marcin Szczuka Rough Sets and Artificial Neural Networks , 1998 .

[17]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[18]  Peter Sussner,et al.  Morphological perceptrons with competitive learning: Lattice-theoretical framework and constructive learning algorithm , 2011, Inf. Sci..

[19]  Mohamed Quafafou,et al.  alpha-RST: a generalization of rough set theory , 2000, Inf. Sci..

[20]  Simon Parsons,et al.  Addendum to "Current Approaches to Handling Imperfect Information in Data and Knowledge Bases" , 1996, IEEE Trans. Knowl. Data Eng..

[21]  George J. Klir,et al.  Uncertainty-Based Information , 1999 .

[22]  Kin Keung Lai,et al.  Variable precision rough set for group decision-making: An application , 2008, Int. J. Approx. Reason..

[23]  Da Ruan,et al.  Probabilistic model criteria with decision-theoretic rough sets , 2011, Inf. Sci..

[24]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[25]  Krzysztof Krawiec,et al.  Neural Networks and Rough Sets - Comparison and Combination for Classification of Histological Pictures , 1993, RSKD.

[26]  Ewa Orłowska,et al.  Studying Incompleteness of Information: A Class of Information Logics , 1998 .

[27]  Rafael Bello,et al.  Feature Selection Algorithms Using Rough Set Theory , 2007, Seventh International Conference on Intelligent Systems Design and Applications (ISDA 2007).

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

[29]  Tsau Young Lin,et al.  A Review of Rough Set Models , 1997 .

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

[31]  Chris Cornelis,et al.  Feature Selection with Fuzzy Decision Reducts , 2008, RSKT.

[32]  A. J. van der Wal,et al.  Discussion on soft computing at FLINS'96 , 1998, Int. J. Intell. Syst..

[33]  Ramin Yasdi,et al.  Combining Rough Sets Learning- and Neural Learning-method to deal with uncertain and imprecise information , 1995, Neurocomputing.

[34]  Wen-Xiu Zhang,et al.  Attribute reduction in ordered information systems based on evidence theory , 2010, Knowledge and Information Systems.

[35]  Tzung-Pei Hong,et al.  Mining fuzzy β-certain and β-possible rules from quantitative data based on the variable precision rough-set model , 2007, Expert Syst. Appl..

[36]  Dominik Slezak,et al.  Rough Sets and Bayes Factor , 2005, Trans. Rough Sets.

[37]  Gian Luigi Ferrari,et al.  Parameterized Structured Operational Semantics , 1998, Fundam. Informaticae.

[38]  Rafael Bello,et al.  Knowledge Discovery Using Rough Set Theory , 2010, Advances in Machine Learning I.

[39]  R. K. Ursem Multi-objective Optimization using Evolutionary Algorithms , 2009 .

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

[41]  Victor W. Marek,et al.  Contributions to the Theory of Rough Sets , 1999, Fundam. Informaticae.

[42]  Yiyu Yao,et al.  On Generalizing Rough Set Theory , 2003, RSFDGrC.

[43]  Qiang Shen,et al.  Selecting informative features with fuzzy-rough sets and its application for complex systems monitoring , 2004, Pattern Recognit..

[44]  Yongsheng Zhao,et al.  Rough Sets in Hybrid Soft Computing Systems , 2007, ADMA.

[45]  Cory J. Butz,et al.  Rough Sets for Uncertainty Reasoning , 2000, Rough Sets and Current Trends in Computing.

[46]  Olve Maudal Preprocessing data for Neural Network based Classifiers - Rough Sets vs Principal Component Analysis , 1996 .

[47]  Rajen B. Bhatt,et al.  On the compact computational domain of fuzzy-rough sets , 2005, Pattern Recognit. Lett..

[48]  Andrzej Skowron,et al.  Approximation Spaces and Information Granulation , 2004, Trans. Rough Sets.

[49]  Honghua Dai,et al.  An Optimal Strategy for Extracting Probabilistic Rules by Combining Rough Sets and Genetic Algorithm , 2003, Discovery Science.

[50]  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 .

[51]  Sudarsan Nanda,et al.  Fuzziness in rough sets , 2000, Fuzzy Sets Syst..

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

[53]  S. K. Wong,et al.  Comparison of the probabilistic approximate classification and the fuzzy set model , 1987 .

[54]  Liang Gao,et al.  An expert system using rough sets theory and self-organizing maps to design space exploration of complex products , 2010, Expert Syst. Appl..

[55]  Chris Cornelis,et al.  Fuzzy Rough Sets: from Theory into Practice , 2008, GrC 2008.

[56]  Marzena Kryszkiewicz,et al.  Rough Set Approach to Incomplete Information Systems , 1998, Inf. Sci..

[57]  Li Jianguo,et al.  Design of a Novel Neural Networks Based On Rough Sets , 2006, 2006 Chinese Control Conference.

[58]  Sankar K. Pal,et al.  Evolutionary modular design of rough knowledge-based network using fuzzy attributes , 2001, Neurocomputing.

[59]  Ching-Hsue Cheng,et al.  A hybrid model based on rough sets theory and genetic algorithms for stock price forecasting , 2010, Inf. Sci..

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

[61]  C. Cornelis,et al.  Vaguely Quantified Rough Sets , 2009, RSFDGrC.

[62]  Maciej Wygralak Rough sets and fuzzy sets—some remarks on interrelations , 1989 .

[63]  Yongquan Wang,et al.  Some implication operators on interval sets and rough sets , 2009, 2009 8th IEEE International Conference on Cognitive Informatics.

[64]  Salvatore Greco,et al.  Parameterized rough set model using rough membership and Bayesian confirmation measures , 2008, Int. J. Approx. Reason..

[65]  Zdzislaw Pawlak,et al.  Rough sets, decision algorithms and Bayes' theorem , 2002, Eur. J. Oper. Res..

[66]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

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

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

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

[70]  Hong-Tae Jeon,et al.  Structure optimization of fuzzy neural network using rough set theory , 1999, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

[71]  Astrid A. Prinz,et al.  Hybridization of Independent Component Analysis, Rough Sets, and Multi-Objective Evolutionary Algorithms for Classificatory Decomposition of Cortical Evoked Potentials , 2006, PRIB.

[72]  Yee Leung,et al.  Connections between rough set theory and Dempster-Shafer theory of evidence , 2002, Int. J. Gen. Syst..

[73]  Rafael Bello,et al.  Two Step Swarm Intelligence to Solve the Feature Selection Problem , 2008, J. Univers. Comput. Sci..

[74]  Yiyu Yao,et al.  Relational Interpretations of Neigborhood Operators and Rough Set Approximation Operators , 1998, Inf. Sci..

[75]  Lotfi A. Zadeh,et al.  Applied Soft Computing - Foreword , 2001, Appl. Soft Comput..

[76]  James L. McClelland Explorations In Parallel Distributed Processing , 1988 .

[77]  Tzung-Pei Hong,et al.  Learning rules from incomplete training examples by rough sets , 2002, Expert Syst. Appl..

[78]  Zdzislaw Pawlak,et al.  VAGUENESS AND UNCERTAINTY: A ROUGH SET PERSPECTIVE , 1995, Comput. Intell..

[79]  Andrzej Skowron,et al.  From the Rough Set Theory to the Evidence Theory , 1991 .

[80]  Sankar K. Pal,et al.  Soft data mining, computational theory of perceptions, and rough-fuzzy approach , 2004, Inf. Sci..

[81]  Eiichiro Tazaki,et al.  Decision Making Using Hybrid Rough Sets and Neural Networks , 2002, Int. J. Neural Syst..

[82]  P. Lingras Rough Neural Networks , 1996 .

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

[84]  Francis Eng Hock Tay,et al.  Economic and financial prediction using rough sets model , 2002, Eur. J. Oper. Res..

[85]  Ching-Hsue Cheng,et al.  Entropy-based fuzzy rough classification approach for extracting classification rules , 2006, Expert Syst. Appl..

[86]  J. Kacprzyk,et al.  Incomplete Information: Rough Set Analysis , 1997 .

[87]  Xiangyang Wang,et al.  Rough set feature selection and rule induction for prediction of malignancy degree in brain glioma , 2006, Comput. Methods Programs Biomed..

[88]  Devendra K. Chaturvedi,et al.  Soft Computing - Techniques and its Applications in Electrical Engineering , 2008, Studies in Computational Intelligence.

[89]  Ramlan Mahmod,et al.  Rough neural expert systems , 2000 .

[90]  Sankar K. Pal,et al.  Rough fuzzy MLP: knowledge encoding and classification , 1998, IEEE Trans. Neural Networks.

[91]  Renpu Li,et al.  Mining classification rules using rough sets and neural networks , 2004, Eur. J. Oper. Res..

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

[93]  Peter Vrancx,et al.  Using ACO and rough set theory to feature selection , 2005 .

[94]  Krzysztof Krawiec,et al.  ROUGH SET REDUCTION OF ATTRIBUTES AND THEIR DOMAINS FOR NEURAL NETWORKS , 1995, Comput. Intell..

[95]  Dominik Slezak,et al.  Neural Networks Design: Rough Set Approach to Continuous Data , 1997, PKDD.

[96]  Lotfi A. Zadeh,et al.  Is there a need for fuzzy logic? , 2008, NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society.

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

[98]  D. Ruan,et al.  Discussion on soft computing at FLINS'96 , 1998 .

[99]  Piero P. Bonissone,et al.  On heuristics as a fundamental constituent of soft computing , 2008, Fuzzy Sets Syst..

[100]  Andrzej Skowron,et al.  Synthesis of Decision Rules for Object Classification , 1998 .

[101]  Carlos A. Coello Coello,et al.  DEMORS: A hybrid multi-objective optimization algorithm using differential evolution and rough set theory for constrained problems , 2010, Comput. Oper. Res..

[102]  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..

[103]  Rafael Bello,et al.  Rough Set Theory Measures for Quality Assessment of a Training Set , 2008 .

[104]  K. Thangavel,et al.  Dimensionality reduction based on rough set theory: A review , 2009, Appl. Soft Comput..

[105]  George J. Klir,et al.  Principles of uncertainty: What are they? Why do we need them? , 1995, Fuzzy Sets Syst..

[106]  Yiyu Yao,et al.  Semantics of Fuzzy Sets in Rough Set Theory , 2004, Trans. Rough Sets.

[107]  Li Pheng Khoo,et al.  Feature extraction using rough set theory and genetic algorithms--an application for the simplification of product quality evaluation , 2002 .

[108]  Andrzej Skowron,et al.  Approximation Spaces and Information Granulation , 2004, Trans. Rough Sets.

[109]  Sankar K. Pal,et al.  Rough-Fuzzy MLP: Modular Evolution, Rule Generation, and Evaluation , 2003, IEEE Trans. Knowl. Data Eng..

[110]  Shuhong Chen,et al.  Study on Discretization in Rough Set Via Modified Quantum Genetic Algorithm , 2008, ICIC.

[111]  Salvatore Greco,et al.  Rough sets theory for multicriteria decision analysis , 2001, Eur. J. Oper. Res..

[112]  Ning Zhong,et al.  Using Rough Sets with Heuristics for Feature Selection , 1999, RSFDGrC.

[113]  Jun Zhao,et al.  New heuristic method for data discretization based on rough set theory , 2009 .

[114]  Tianxu Zhang,et al.  A Hybrid Method for Relevance Feedback in Image Retrieval Using Rough Sets and Neural Networks , 2005 .

[115]  Thomas E. McKee,et al.  Genetic programming and rough sets: A hybrid approach to bankruptcy classification , 2002, Eur. J. Oper. Res..

[116]  Wei-Zhi Wu,et al.  Knowledge reduction in random information systems via Dempster-Shafer theory of evidence , 2005, Inf. Sci..

[117]  Y. Yao,et al.  Generalized Rough Set Models , 1998 .

[118]  Andrzej Skowron,et al.  Towards a Rough Mereology-Based Logic for Approximate Solution Synthesis. Part 1 , 1997, Stud Logica.

[119]  Piero P. Bonissone,et al.  Soft computing: the convergence of emerging reasoning technologies , 1997, Soft Comput..

[120]  Sankar K. Pal,et al.  Roughness of a Fuzzy Set , 1996, Inf. Sci..

[121]  T. Iwiński Algebraic approach to rough sets , 1987 .

[122]  Qiang Shen,et al.  Finding Rough Set Reducts with Ant Colony Optimization , 2003 .

[123]  Roman W. Swiniarski,et al.  Rough Sets and Neural Networks Application to Handwritten Character Recognition by Complex Zernike Moments , 1998, Rough Sets and Current Trends in Computing.

[124]  Li Pheng Khoo,et al.  A prototype genetic algorithm-enhanced rough set-based rule induction system , 2001, Comput. Ind..

[125]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[126]  Andrzej Skowron,et al.  Rough sets: Some extensions , 2007, Inf. Sci..

[127]  Rafael Bello,et al.  A method to build similarity relations into extended Rough Set Theory , 2010, 2010 10th International Conference on Intelligent Systems Design and Applications.

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

[129]  Piero P. Bonissone,et al.  Editorial: Reasoning with Uncertainty in Expert Systems , 1985, Int. J. Man Mach. Stud..

[130]  Zongyuan Mao,et al.  A new algorithm for neural network architecture study , 2000, Proceedings of the 3rd World Congress on Intelligent Control and Automation (Cat. No.00EX393).

[131]  Dimitris A. Karras,et al.  Revisiting the Problem of Weight Initialization for Multi-Layer Perceptrons Trained with Back Propagation , 2008, ICONIP.

[132]  Yiyu Yao,et al.  A Comparative Study of Fuzzy Sets and Rough Sets , 1998 .

[133]  Yiyu Yao,et al.  Interval sets and interval-set algebras , 2009, 2009 8th IEEE International Conference on Cognitive Informatics.

[134]  Rafael Bello,et al.  Feature Selection through Dynamic Mesh Optimization , 2008, CIARP.

[135]  J. Grzymala-Busse,et al.  Rough Set Approaches to Rule Induction from Incomplete Data , 2004 .