On relationship between probabilistic rough set and Bayesian risk decision over two universes

References

• Beynon , M. , Peel , M.J. and Tang , Y.C. 2004 . The application of fuzzy decision tree analysis in an exposition of the antecedents of audit fees . Omega , 32 ( 3 ) : 231 – 244 .
   Web of Science ®Google Scholar
• Duda , R.O. and Hart , P.E. 1973 . Pattern Classification and Scene Analysis , New York : Wiley .
   Google Scholar
• Duntsch , I. and Gediga , G.R. 2001 . Rough information analysis . International journal of intelligent systems , 16 : 121 – 147 .
   Web of Science ®Google Scholar
• Fishburn , P. 1988 . Nonlinear Peferences and Utility Theory , Baltimore, MD : The John Hopkins University Press .
   Google Scholar
• Gong , Z.T. and Shi , Z.H. 2008 . On the covering probabilistic rough set models and its Bayes decisions . Fuzzy systems and mathematics , 22 ( 4 ) : 142 – 148 . (in Chinese)
   Google Scholar
• Gong , Z.T. and Sun , B.Z. 2008 . Probability rough sets model between different universes and its applications . International Conference on Machine Learning and Cybernetics , : 561 – 565 .
   Google Scholar
• Li , X.H. and Zhang , D.S. 2006 . Determination and interpretation of the threshold value in (α − β)-rough set model . Journal of Shandong University , 36 ( 2 ) : 81 – 85 . (Engineering Science) (In Chinese)
   Google Scholar
• Ma, W.M. and Sun, B.Z., 2011. Probabilistic rough sets over two universes and rough entropy, International journal of approximate reasoning (submitted)
   Google Scholar
• Neumann , V.J. and Morgenstern , O. 1947 . The Theory of Games and Economic Behavior , 2nd ed. , Princeton, NJ : Princeton University of Press .
   Google Scholar
• Pawlak , Z. 1982 . Rough sets . International journal of information science , 11 ( 5 ) : 341 – 356 .
   Web of Science ®Google Scholar
• Pawlak , Z. 1991 . Rough sets: theoretical aspects of reasoning about data, system theory, knowledge engineering and problem solving , Dordrecht : Kluwer .
   Google Scholar
• Pawlak , Z. 2002 . Rough sets, decision algorithms and Bayesian' theorem . European journal of operational research , 136 : 181 – 189 .
   Web of Science ®Google Scholar
• Pawlak , Z. 2004 . Decision rules and flow networks . European journal of operational research , 154 : 184 – 190 .
   Web of Science ®Google Scholar
• Pawlak , Z. 2007a . Rudiments of rough sets . Information sciences , 177 ( 1 ) : 3 – 27 .
   Web of Science ®Google Scholar
• Pawlak , Z. 2007b . Rough sets: some extensions . Information sciences , 177 ( 1 ) : 28 – 40 .
   Web of Science ®Google Scholar
• Pawlak , Z. 2007c . Rough sets and Boolean reasoning . Information sciences , 177 ( 1 ) : 41 – 73 .
   Web of Science ®Google Scholar
• Pawlak , Z. and Skowron , A. 1994 . “ Rough membership functions ” . In Advances in the Dempster–Shafer Theory of Evidence , Edited by: Yager , R.R. , Fedrizzi , M. and Kacprzyk , J. 251 – 271 . New York : John Wiley and Sons .
   Google Scholar
• Pawlak , Z. , Wong , S.K.M. and Ziarko , W. 1988 . Rough sets: probabilistic versus deterministic approach . International journal of man–machine studies , 29 : 81 – 95 .
   Google Scholar
• Polkowski , L. and Skowron , A. 1996 . Rough mereology: a new paradigm for approximate reasoning . International journal of approximate reasoning , 15 : 333 – C365 .
   Web of Science ®Google Scholar
• Savage , L. 1954 . The foundations of statistics , New York : Wiley .
   Google Scholar
• Sun, B.Z. and Ma, W.M., 2011. Conflict analysis decision based on rough sets theory over two universes, Knowledge-based systems (submitted)
   Google Scholar
• Szelak , D. and Ziarko , W. 2005 . The investigation of the Bayesian rough set model . International journal of approximate reasoning , 40 ( 1–2 ) : 81 – 91 .
   Web of Science ®Google Scholar
• Tseng , T.L. and Huang , C.C. 2007 . Rough set-based approach to feature selection in customer relationship management . Omega , 35 ( 4 ) : 365 – 383 .
   Web of Science ®Google Scholar
• Tsumoto , S. 1998 . Automated extraction of medical expert system rules from clinical databases based on rough set theory . Information sciences , 112 : 67 – 84 .
   Web of Science ®Google Scholar
• Tsumoto , S. 2004 . Mining diagnostic rules from clinical databases using rough sets and medical diagnostic model . Information science , 162 ( 2 ) : 65 – 80 .
   Web of Science ®Google Scholar
• Wong , S.K.M. and Ziarko , W. 1987 . Comparison of the probabilistic approximate classification and the fuzzy set model . Fuzzy sets and systems , 21 : 357 – 362 .
   Web of Science ®Google Scholar
• Yan , J.A. 1998 . Theory of measures , Beijing : Science Press .
   Google Scholar
• Yao , Y.Y. 2001 . Information granulation and rough set approximation . International journal of intelligent systems , 16 : 87 – 104 .
   Web of Science ®Google Scholar
• Yao , Y.Y . 2003 . “ Information granulation and approximation in a decision-theoretical model of rough sets ” . In Rough-neural computing: techniques for computing with words , Edited by: Pal , S.K. , Polkowski , L. and Skowron , A. 491 – 518 . Berlin : Springer .
   Google Scholar
• Yao , Y.Y. 2008 . Probabilistic rough set approximations . International journal of approximate reasoning , 49 ( 2 ) : 255 – 271 .
   Web of Science ®Google Scholar
• Yao , Y.Y. 2010 . Three-way decision with probabilistic rough set . Informtion sciences , 180 : 341 – 353 .
   Web of Science ®Google Scholar
• Yao , Y.Y. , Wong , S.K.M. and Lin , T.Y. 1997 . “ A review of rough set models ” . In Rough sets and data mining: analysis for imprecise data , Edited by: Lin , T.Y. and Cercone , N. 47 – 75 . Boston : Kluwer Academic Publishers .
   Google Scholar
• Yao , Y.Y. , Wong , S.K.M. and Lingras , P.J. 1990 . “ A decision-theoretic rough set model ” . In Methodologies for intelligent systems , Edited by: Ras , Z.W. , Zemankova , M. and Emrich , M.L. Vol. 5 , 17 – 24 . New York : North-Holland .
   Google Scholar
• Yao , Y.Y. and Wong , S.K.M. 1992 . A decision theoretic framework for approximating concepts . International journal of man-machine studies , 37 : 793 – 809 .
   Google Scholar
• Yao , J.T. , Yao , Y.Y. and Ziarko , W. 2008 . Probabilistic rough sets: approximations, decision-makings, and applications . International journal of approximate reasoning , 49 ( 2 ) : 253 – 254 .
   Web of Science ®Google Scholar
• Zaras , K. 2004 . Rough approximation of a preference relation by a multi-attribute dominance for deterministic stochastic and fuzzy decision problems . European journal of operational research , 159 : 196 – 206 .
   Web of Science ®Google Scholar
• Zhang , W.X. 2001 . Rough Set Theory and Methodology , Beijing : Science Press .
   Google Scholar
• Zhu , D. 2001 . Data mining for network intrusion detection: a comparison of alternative methods . Decision sciences , 32 ( 4 ) : 635 – 660 .
   Web of Science ®Google Scholar
• Ziarko , W. 2008 . Probabilistic approach to rough sets . International journal of approximate reasoning , 49 ( 2 ) : 272 – 284 .
   Web of Science ®Google Scholar