Rough Sets and Three-Way Decisions

The notion of three-way decisions was originally introduced by the needs to explain the three regions of probabilistic rough sets. Recent studies show that rough set theory is only one of possible ways to construct three regions. A more general theory of three-way decisions has been proposed, embracing ideas from rough sets, interval sets, shadowed sets, three-way approximations of fuzzy sets, orthopairs, square of oppositions, and others. This paper presents a trisecting-and-acting framework of three-way decisions. With respect to trisecting, we divide a universal set into three regions. With respect to acting, we design most effective strategies for processing the three regions. The identification and explicit investigation of different strategies for different regions are a distinguishing feature of three-way decisions.

[1]  Yiyu Yao,et al.  Granular Computing and Sequential Three-Way Decisions , 2013, RSKT.

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

[3]  Nouman Azam,et al.  Web-Based Medical Decision Support Systems for Three-Way Medical Decision Making With Game-Theoretic Rough Sets , 2015, IEEE Transactions on Fuzzy Systems.

[4]  Didier Dubois,et al.  Borderline vs. unknown: comparing three-valued representations of imperfect information , 2014, Int. J. Approx. Reason..

[5]  Davide Ciucci.  Orthopairs in the 1960s: Historical Remarks and New Ideas , 2014, RSCTC.

[6]  Ali Shakiba,et al.  S-approximation Spaces: A Three-way Decision Approach , 2015, Fundam. Informaticae.

[7]  Didier Dubois,et al.  Oppositions in Rough Set Theory , 2012, RSKT.

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

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

[10]  Decui Liang,et al.  A novel three-way decision model based on incomplete information system , 2016, Knowl. Based Syst..

[11]  Hong-Ying Zhang,et al.  Ranking interval sets based on inclusion measures and applications to three-way decisions , 2016, Knowl. Based Syst..

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

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

[14]  Xiaofei Deng.  Three-Way Classification Models , 2015 .

[15]  Huaxiong Li,et al.  Risk Decision Making Based on Decision-theoretic Rough Set: A Three-way View Decision Model , 2011, Int. J. Comput. Intell. Syst..

[16]  Bao Qing Hu,et al.  Three-way decisions space and three-way decisions , 2014, Inf. Sci..

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

[18]  Witold Pedrycz,et al.  Shadowed sets: representing and processing fuzzy sets , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[19]  Vijay V. Raghavan,et al.  A Comprehensive Granular Model for Decision Making with Complex , 2015 .

[20]  Jie Lu,et al.  Multi-Level Decision Making: Models, Methods and Applications , 2015 .

[21]  Decui Liang,et al.  Deriving three-way decisions from intuitionistic fuzzy decision-theoretic rough sets , 2015, Inf. Sci..

[22]  Yiyu Yao,et al.  The two sides of the theory of rough sets , 2015, Knowl. Based Syst..

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

[24]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[25]  Fan Min,et al.  Three-way recommender systems based on random forests , 2016, Knowl. Based Syst..

[26]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[27]  Jerzy W. Grzymala-Busse,et al.  Probabilistic rule induction with the LERS data mining system , 2011, Int. J. Intell. Syst..

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

[29]  Yiyu Yao,et al.  Generalization of Rough Sets using Modal Logics , 1996, Intell. Autom. Soft Comput..

[30]  James F. Peters,et al.  Proximal three-way decisions: Theory and applications in social networks , 2016, Knowl. Based Syst..

[31]  Guoyin Wang,et al.  A tree-based incremental overlapping clustering method using the three-way decision theory , 2016, Knowl. Based Syst..

[32]  Jiye Liang,et al.  Decision-theoretic rough sets under dynamic granulation , 2016, Knowl. Based Syst..

[33]  Yiyu Yao,et al.  Duality in Rough Set Theory Based on the Square of Opposition , 2013, Fundam. Informaticae.

[34]  Didier Dubois,et al.  From Blanché’s Hexagonal Organization of Concepts to Formal Concept Analysis and Possibility Theory , 2012, Logica Universalis.

[35]  Yao Li,et al.  TDUP: an approach to incremental mining of frequent itemsets with three-way-decision pattern updating , 2015, International Journal of Machine Learning and Cybernetics.

[36]  Zdzislaw Pawlak,et al.  Rough classification , 1984, Int. J. Hum. Comput. Stud..

[37]  Davide Ciucci,et al.  Orthopairs: A Simple and Widely UsedWay to Model Uncertainty , 2011, Fundam. Informaticae.

[38]  Haiyan Zhao,et al.  An approach to emergency decision making based on decision-theoretic rough set over two universes , 2016, Soft Comput..

[39]  Jingtao Yao,et al.  A Scientometrics Study of Rough Sets in Three Decades , 2013, RSKT.

[40]  Yiyu Yao,et al.  Interval-set algebra for qualitative knowledge representation , 1993, Proceedings of ICCI'93: 5th International Conference on Computing and Information.

[41]  Bing Huang,et al.  Sequential three-way decision and granulation for cost-sensitive face recognition , 2016, Knowl. Based Syst..

[42]  Brian F. Chellas.  Modal Logic: Normal systems of modal logic , 1980 .

[43]  Tianrui Li,et al.  Dynamic Maintenance of Three-Way Decision Rules , 2014, RSKT.

[44]  Yiyu Yao,et al.  Decision-theoretic three-way approximations of fuzzy sets , 2014, Inf. Sci..

[45]  Ewa Orlowska,et al.  Representation of Nondeterministic Information , 1984, Theor. Comput. Sci..