Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
10.1007/978-3-030-22815-6_1guideproceedingsArticle/Chapter ViewAbstractPublication PagesConference Proceedingsacm-pubtype
Article

An Application of Bayesian Confirmation Theory for Three-Way Decision

Published: 17 June 2019 Publication History

Abstract

Bayesian confirmation theory studies how a piece of evidence confirms a hypothesis. In a qualitative approach, a piece of evidence may confirm, disconfirm, or be neutral with respect to a hypothesis. A quantitative approach uses Bayesian confirmation measures to evaluate the degree to which a piece of evidence confirms a hypothesis. In both approaches, we may perform a three-way classification of a set of pieces of evidence for a given hypothesis. The set of evidence is divided into three regions of positive evidence that confirms the hypothesis, negative evidence that disconfirms the hypothesis, and neutral evidence that neither confirms nor disconfirms the hypothesis. In this paper, we investigate three-way classification models in both qualitative and quantitative Bayesian confirmation approaches and explore their relationships to three-way classification models in rough set theory.

References

[1]
Afridi MK, Azam N, Yao JT, and Alanazi E A three-way clustering approach for handling missing data using GTRS Int. J. Approx. Reason. 2018 98 11-24
[2]
Azam N and Yao JT Game-theoretic rough sets for recommender systems Knowl.-Based Syst. 2014 72 96-107
[3]
Bryniarski E A calculus of rough sets of the first order Bull. Pol. Acad. Sci. Math. 1989 37 71-78
[4]
Festa R Galavotti MC and Pagnini A Bayesian confirmation Experience, Reality, and Scientific Explanation 1999 Dordrecht Springer 55-87
[5]
Fitelson, B.: Studies in Bayesian confirmation theory. Ph.D. dissertation, University of Wisconsin (2001). http://fitelson.org/thesis.pdf
[6]
Greco S, Matarazzo B, and Słowiński R Parameterized rough set model using rough membership and Bayesian confirmation measures Int. J. Approx. Reason. 2008 49 285-300
[7]
Greco S, Matarazzo B, and Słowiński R Ślęzak D, Wang G, Szczuka M, Düntsch I, and Yao YY Rough membership and Bayesian confirmation measures for parameterized rough sets Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing 2005 Heidelberg Springer 314-324
[8]
Greco S, Pawlak Z, and Słowiński R Can Bayesian confirmation measures be useful for rough set decision rules? Eng. Appl. Artif. Intell. 2004 17 345-361
[9]
Greco S, Słowiński R, and Szczęch I Measures of rule interestingness in various perspectives of confirmation Inf. Sci. 2016 346–347 216-235
[10]
Greco S, Słowiński R, and Szczęch I Finding meaningful Bayesian confirmation measures Fundam. Inf. 2013 127 161-176
[11]
Hu MJ and Yao YY Structured approximations as a basis for three-way decisions with rough sets Knowl.-Based Syst. 2019 165 92-109
[12]
Jia XY, Shang L, Zhou B, and Yao YY Generalized attribute reduct in rough set theory Knowl.-Based Syst. 2016 91 204-218
[13]
Li HX, Zhang LB, Huang B, and Zhou XZ Sequential three-way decision and granulation for cost-sensitive face recognition Knowl.-Based Syst. 2016 91 241-251
[14]
Ma WM and Sun BZ Probabilistic rough set over two universes and rough entropy Int. J. Approx. Reason. 2012 53 608-619
[15]
Ma X and Yao YY Three-way decision perspectives on class-specific attribute reducts Inf. Sci. 2018 450 227-245
[16]
Ma JM, Zou CJ, and Pan XC Structured probabilistic rough set approximations Int. J. Approx. Reason. 2017 90 319-332
[17]
Pawlak Z Rough Sets: Theoretical Aspects of Reasoning about Data 1991 Boston Kluwer Academic Publishers
[18]
Pawlak Z Rough sets Int. J. Comput. Inf. Sci. 1982 11 341-356
[19]
Qi JJ, Qian T, and Wei L The connections between three-way and classical concept analysis Knowl.-Based Syst. 2016 91 143-151
[20]
Qian YH, Liang JY, Pedrycz W, and Dang C Positive approximation: An accelerator for attribute reduction in rough set theory Artif. Intell. 2010 174 597-618
[21]
Ren RS and Wei L The attribute reductions of three-way concept lattices Knowl.-Based Syst. 2016 99 92-102
[22]
Sun BZ, Ma WM, and Xiao X Three-way group decision making based on multigranulation fuzzy decision-theoretic rough set over two universes Int. J. Approx. Reason. 2017 81 87-102
[23]
Yao YY Three-way decision and granular computing Int. J. Approx. Reason. 2018 103 107-123
[24]
Yao YY Probabilistic rough set approximations Int. J. Approx. Reason. 2008 49 255-271
[25]
Yao YY, Hu MJ, and Deng XF Medina J, Ojeda-Aciego M, Verdegay JL, Pelta DA, Cabrera IP, Bouchon-Meunier B, and Yager RR Modes of sequential three-way classifications Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations 2018 Cham Springer 724-735
[26]
Yao YY and Zhou B Two Bayesian approaches to rough sets Eur. J. Oper. Res. 2016 251 904-917
[27]
Yu H Polkowski L, Yao YY, Artiemjew P, Ciucci D, Liu D, Ślęzak D, and Zielosko B A framework of three-way cluster analysis Rough Sets 2017 Cham Springer 300-312
[28]
Yu H, Zhang C, and Wang GY A tree-based incremental overlapping clustering method using the three-way decision theory Knowl.-Based Syst. 2016 91 189-203
[29]
Zhang HR and Min F Three-way recommender systems based on random forests Knowl.-Based Syst. 2016 91 275-286
[30]
Zhou, B.: A cost-sensitive approach to ternary classification. Ph.D. dissertation, University of Regina (2012)
[31]
Zhou B and Yao YY Lingras P, Wolski M, Cornelis C, Mitra S, and Wasilewski P Comparison of two models of probabilistic rough sets Rough Sets and Knowledge Technology 2013 Heidelberg Springer 121-132

Cited By

View all

Recommendations

Comments

Information & Contributors

Information

Published In

cover image Guide Proceedings
Rough Sets: International Joint Conference, IJCRS 2019, Debrecen, Hungary, June 17–21, 2019, Proceedings
Jun 2019
565 pages
ISBN:978-3-030-22814-9
DOI:10.1007/978-3-030-22815-6

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 17 June 2019

Author Tags

  1. Three-way decision
  2. Bayesian confirmation
  3. Rough set
  4. Attribute reduct

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 13 Sep 2024

Other Metrics

Citations

Cited By

View all

View Options

View options

Get Access

Login options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media