Three-way attribute reducts

Abstract Three-way decisions are a fundamental methodology with extensive applications, while attribute reducts play an important role in data analyses. The combination of both topics has theoretical significance and applicable prospects, but rarely gains direct research at present. In this paper, three-way decisions are introduced into attribute reducts and thus three-way attribute reducts are systematically investigated. Firstly, classical qualitative reducts are reviewed by the dependency degree. Then, the dependency degree implements approximation analyses to be improved to a controllable measure: the relative dependency degree, which is monotonic to relatively measure the attribute dependency. Given an approximate bar, the relative dependency degree defines the applicable quantitative reducts, which approach, expand, and weaken the classical qualitative reducts. This type of quantitative reducts is actually the positive quantitative reducts for three-way reducts. Thus, three-way quantitative reducts are established by the relative dependency degree and dual thresholds. The positive, boundary, and negative quantitative reducts divide the power set of the condition attribute set and thus gain acceptance, noncommitment, and rejection decisions, respectively; they exhibit the potential derivation from the higher level to the lower level. Furthermore, three-way qualitative reducts are established by degeneration to implement three-way decisions, and three-way quantitative and qualitative reducts exhibit the approximation, expansion, and strength; by virtue of superiority analyses, three-way reducts improve the latent two-way reducts with only acceptance and rejection decisions. Finally, three-way reducts are practically illustrated by observing an example of decision tables. By developing the relative dependency degree with controllability, three-way reducts implement both a quantitative generalization for qualitative reducts and a structural completion for attribute reducts. The relevant study provides a new insight into both three-way decisions and attribute reducts.

[1]  A. V. Savchenko,et al.  Fast multi-class recognition of piecewise regular objects based on sequential three-way decisions and granular computing , 2016, Knowl. Based Syst..

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

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

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

[5]  Jiye Liang,et al.  A new measure of uncertainty based on knowledge granulation for rough sets , 2009, Inf. Sci..

[6]  Jakub Wroblewski,et al.  Ensembles of Classifiers Based on Approximate Reducts , 2001, Fundam. Informaticae.

[7]  Yee Leung,et al.  Granular Computing and Knowledge Reduction in Formal Contexts , 2009, IEEE Transactions on Knowledge and Data Engineering.

[8]  Yiyu Yao,et al.  A Note on Attribute Reduction in the Decision-Theoretic Rough Set Model , 2011, Trans. Rough Sets.

[9]  Zhifei Zhang,et al.  A three-way decisions model with probabilistic rough sets for stream computing , 2017, Int. J. Approx. Reason..

[10]  Bing Huang,et al.  Hierarchical structures and uncertainty measures for intuitionistic fuzzy approximation space , 2016, Inf. Sci..

[11]  Guoyin Wang,et al.  A Comparative Study of Algebra Viewpoint and Information Viewpoint in Attribute Reduction , 2005, Fundam. Informaticae.

[12]  Yiyu Yao,et al.  Class-specific attribute reducts in rough set theory , 2017, Inf. Sci..

[13]  Nan Zhang,et al.  Attribute reduction for sequential three-way decisions under dynamic granulation , 2017, Int. J. Approx. Reason..

[14]  Weihua Xu,et al.  Generalized multigranulation double-quantitative decision-theoretic rough set , 2016, Knowl. Based Syst..

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

[16]  Duoqian Miao,et al.  Quantitative/qualitative region-change uncertainty/certainty in attribute reduction: Comparative region-change analyses based on granular computing , 2016, Inf. Sci..

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

[18]  Zhongzhi Shi,et al.  On quick attribute reduction in decision-theoretic rough set models , 2016, Inf. Sci..

[19]  Duoqian Miao,et al.  Region-based quantitative and hierarchical attribute reduction in the two-category decision theoretic rough set model , 2014, Knowl. Based Syst..

[20]  Yiyu Yao,et al.  Two Bayesian approaches to rough sets , 2016, Eur. J. Oper. Res..

[21]  Zhang Wen-xiu,et al.  Attribute reduction theory and approach to concept lattice , 2005 .

[22]  Yiyu Yao,et al.  Probabilistic Rough Sets , 2015, Handbook of Computational Intelligence.

[23]  Jiye Liang,et al.  Ieee Transactions on Knowledge and Data Engineering 1 a Group Incremental Approach to Feature Selection Applying Rough Set Technique , 2022 .

[24]  Dominik Slezak,et al.  Approximate Reducts in Decision Tables , 1996 .

[25]  Yumin Chen,et al.  Three-way decision reduction in neighborhood systems , 2016, Appl. Soft Comput..

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

[27]  Tao Feng,et al.  Variable precision multigranulation decision-theoretic fuzzy rough sets , 2016, Knowl. Based Syst..

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

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

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

[31]  Ling Wei,et al.  The connections between three-way and classical concept lattices , 2016, Knowl. Based Syst..

[32]  Yiyu Yao,et al.  Rough Sets and Three-Way Decisions , 2015, RSKT.

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

[34]  Jesús Medina,et al.  Attribute reduction in multi-adjoint concept lattices , 2015, Inf. Sci..

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

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

[37]  Wen-Xiu Zhang,et al.  Attribute reduction theory and approach to concept lattice , 2007, Science in China Series F: Information Sciences.

[38]  Witold Pedrycz,et al.  Positive approximation: An accelerator for attribute reduction in rough set theory , 2010, Artif. Intell..

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

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

[41]  In-Kyoo Park,et al.  Rough set approach for clustering categorical data using information-theoretic dependency measure , 2015, Inf. Syst..

[42]  Decui Liang,et al.  Three-way group decisions with decision-theoretic rough sets , 2016, Inf. Sci..

[43]  Hung Son Nguyen,et al.  Searching for Reductive Attributes in Decision Tables , 2015, Trans. Rough Sets.

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

[45]  Dominik Slezak,et al.  Approximate Entropy Reducts , 2002, Fundam. Informaticae.

[46]  Yiyu Yao,et al.  Cost-sensitive three-way email spam filtering , 2013, Journal of Intelligent Information Systems.

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

[48]  Wen-Xiu Zhang,et al.  Knowledge reduction based on the equivalence relations defined on attribute set and its power set , 2007, Inf. Sci..

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

[50]  Duoqian Miao,et al.  Quantitative information architecture, granular computing and rough set models in the double-quantitative approximation space of precision and grade , 2014, Inf. Sci..

[51]  Duoqian Miao,et al.  Three-layer granular structures and three-way informational measures of a decision table , 2017, Inf. Sci..

[52]  Heung Wong,et al.  On two novel types of three-way decisions in three-way decision spaces , 2017, Int. J. Approx. Reason..

[53]  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.

[54]  Ling Li,et al.  Attribute reduction approaches for general relation decision systems , 2015, Pattern Recognit. Lett..

[55]  Yiyu Yao,et al.  Relative reducts in consistent and inconsistent decision tables of the Pawlak rough set model , 2009, Inf. Sci..

[56]  Duoqian Miao,et al.  Double-quantitative fusion of accuracy and importance: Systematic measure mining, benign integration construction, hierarchical attribute reduction , 2016, Knowl. Based Syst..

[57]  Rajen B. Bhatt,et al.  On the extension of functional dependency degree from crisp to fuzzy partitions , 2006, Pattern Recognit. Lett..

[58]  Bao Qing Hu,et al.  Three-way decisions based on semi-three-way decision spaces , 2017, Inf. Sci..

[59]  Feng Jiang,et al.  A relative decision entropy-based feature selection approach , 2015, Pattern Recognit..

[60]  Yiyu Yao,et al.  An Addition Strategy for Reduct Construction , 2014, RSKT.

[61]  Masahiro Inuiguchi,et al.  Variable-precision dominance-based rough set approach and attribute reduction , 2009, Int. J. Approx. Reason..

[62]  Bao Qing Hu,et al.  Fuzzy and interval-valued fuzzy decision-theoretic rough set approaches based on fuzzy probability measure , 2015, Inf. Sci..

[63]  Yiyu Yao,et al.  Generalized attribute reduct in rough set theory , 2016, Knowl. Based Syst..

[64]  Guoyin Wang,et al.  Decision region distribution preservation reduction in decision-theoretic rough set model , 2014, Inf. Sci..

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