Three-Way Decisions in Stochastic Decision-Theoretic Rough Sets

In the previous decision-theoretic rough sets (DTRS), its loss function values are precise. This paper extends the precise values of loss functions to a more realistic stochastic environment. The stochastic loss functions are induced to decision-theoretic rough set theory based on the bayesian decision theory. A model of stochastic decision-theoretic rough set theory (SDTRS) is built with respect to the minimum bayesian expected risk. The corresponding propositions and criteria of SDTRS are also analyzed. Furthermore, we investigate two special SDTRS models under the uniform distribution and the normal distribution, respectively. Finally, an empirical study of Public-Private Partnerships (PPP) project investment validates the reasonability and effectiveness of the proposed models.

[1]  Tianrui Li,et al.  THREE-WAY GOVERNMENT DECISION ANALYSIS WITH DECISION-THEORETIC ROUGH SETS , 2012 .

[2]  Yiyu Yao,et al.  A Note on Attribute Reduction in the Decision-Theoretic Rough Set Model , 2008, RSCTC.

[3]  Decui Liang,et al.  A New Discriminant Analysis Approach under Decision-Theoretic Rough Sets , 2011, RSKT.

[4]  M. Beynon,et al.  Variable precision rough set theory and data discretisation: an application to corporate failure prediction , 2001 .

[5]  Chris Cornelis,et al.  Rough Sets and Intelligent Systems Paradigms , 2014, Lecture Notes in Computer Science.

[6]  Yiyu Yao,et al.  A Three-Way Decision Approach to Email Spam Filtering , 2010, Canadian Conference on AI.

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

[8]  Fiona Macmillan,et al.  Risk, uncertainty and investment decision-making in the upstream oil and gas industry , 2000 .

[9]  J. Kassirer,et al.  The threshold approach to clinical decision making. , 1980, The New England journal of medicine.

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

[11]  Sadaaki Miyamoto,et al.  Rough Sets and Current Trends in Computing , 2012, Lecture Notes in Computer Science.

[12]  S. K. Michael Wong,et al.  Rough Sets: Probabilistic versus Deterministic Approach , 1988, Int. J. Man Mach. Stud..

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

[14]  Wuyi Yue,et al.  Dynamic risk management in petroleum project investment based on a variable precision rough set model , 2010 .

[15]  Bing Zhou.  A New Formulation of Multi-category Decision-Theoretic Rough Sets , 2011, RSKT.

[16]  William Zhu,et al.  Attribute reduction of data with error ranges and test costs , 2012, Inf. Sci..

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

[18]  Haibo He,et al.  Advances in Neural Networks – ISNN 2009 , 2009, Lecture Notes in Computer Science.

[19]  Jerzy W. Grzymala-Busse,et al.  Transactions on Rough Sets XIII , 2011, Lecture Notes in Computer Science.

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

[21]  Yiyu Yao,et al.  The superiority of three-way decisions in probabilistic rough set models , 2011, Inf. Sci..

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

[23]  Yiyu Yao,et al.  An Outline of a Theory of Three-Way Decisions , 2012, RSCTC.

[24]  Rob Goudey,et al.  Do statistical inferences allowing three alternative decisions give better feedback for environmentally precautionary decision-making? , 2007, Journal of environmental management.

[25]  Yuhua Qian,et al.  Test-cost-sensitive attribute reduction , 2011, Inf. Sci..

[26]  Huaxiong Li,et al.  Risk Decision Making Based on Decision-theoretic Rough Set: A Three-way View Decision Model , 2011 .

[27]  Min Chen,et al.  Semi-supervised Rough Cost/Benefit Decisions , 2009, Fundam. Informaticae.

[28]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[29]  Yiyu Yao,et al.  Naive Bayesian Rough Sets , 2010, RSKT.

[30]  Andrzej Skowron,et al.  Transactions on Rough Sets III , 2005, Trans. Rough Sets.

[31]  Jingtao Yao,et al.  Web-Based Support Systems with Rough Set Analysis , 2007, RSEISP.

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

[33]  Wenqing Zhao,et al.  An Email Classification Scheme Based on Decision-Theoretic Rough Set Theory and Analysis of Email Security , 2005, TENCON 2005 - 2005 IEEE Region 10 Conference.

[34]  Liu Juan,et al.  Supporting E-Learning System with Modified Bayesian Rough Set Model , 2009, ISNN.

[35]  Dun Liu,et al.  A Multiple-category Classification Approach with Decision-theoretic Rough Sets , 2012, Fundam. Informaticae.

[36]  Zhenmin Tang,et al.  Minimum cost attribute reduction in decision-theoretic rough set models , 2013, Inf. Sci..

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

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

[39]  Decui Liang,et al.  Fuzzy interval decision-theoretic rough sets , 2013, 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS).

[40]  Yiyu Yao,et al.  Three-Way Decision: An Interpretation of Rules in Rough Set Theory , 2009, RSKT.

[41]  Jingtao Yao,et al.  Modelling Multi-agent Three-way Decisions with Decision-theoretic Rough Sets , 2012, Fundam. Informaticae.

[42]  Yiyu Yao,et al.  Three-way Investment Decisions with Decision-theoretic Rough Sets , 2011, Int. J. Comput. Intell. Syst..

[43]  M. Forster,et al.  Key Concepts in Model Selection: Performance and Generalizability. , 2000, Journal of mathematical psychology.

[44]  Zhou Xianzhong,et al.  Two decades'research on decision-theoretic rough sets , 2010, 9th IEEE International Conference on Cognitive Informatics (ICCI'10).

[45]  Witold Pedrycz,et al.  International Journal of Approximate Reasoning Triangular Fuzzy Decision-theoretic Rough Sets , 2022 .

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

[47]  Yiyu Yao,et al.  An Information-Theoretic Interpretation of Thresholds in Probabilistic Rough Sets , 2012, RSKT.

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

[49]  Li Hua-xiong,et al.  Interval-valued Decision-theoretic Rough Sets , 2012 .

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

[51]  Bingzhen Sun,et al.  On relationship between probabilistic rough set and Bayesian risk decision over two universes , 2012, Int. J. Gen. Syst..

[52]  Decui Liang,et al.  Decision-Theoretic Rough Sets with Probabilistic Distribution , 2012, RSKT.

[53]  Decui Liang,et al.  Incorporating logistic regression to decision-theoretic rough sets for classifications , 2014, Int. J. Approx. Reason..

[54]  Dun Liu,et al.  Non-Monotonic Attribute Reduction in Decision-Theoretic Rough Sets , 2013, Fundam. Informaticae.

[55]  Jingtao Yao,et al.  Game-Theoretic Rough Sets , 2011, Fundam. Informaticae.

[56]  Yiyu Yao,et al.  Two Semantic Issues in a Probabilistic Rough Set Model , 2011, Fundam. Informaticae.

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

[58]  Frank S. T. Hsiao,et al.  Production-sharing contracts and decision-making in oil production: The case of Indonesia , 1993 .

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

[60]  Piotr Synak,et al.  Brighthouse: an analytic data warehouse for ad-hoc queries , 2008, Proc. VLDB Endow..

[61]  Liu Dun,et al.  Fuzzy Decision-theoretic Rough Sets , 2012 .

[62]  Philip W. Woodward,et al.  An application of Bayesian methods in SPC , 1993 .

[63]  Mohamed M. E. Abd El-Monsef,et al.  Decision Analysis via Granulation Based on General Binary Relation , 2007, Int. J. Math. Math. Sci..

[64]  Arul Mishra,et al.  In Praise of Vagueness , 2010, Psychological science.

[65]  Min Chen,et al.  Rough Cluster Quality Index Based on Decision Theory , 2009, IEEE Transactions on Knowledge and Data Engineering.