We extend the fuzzy rough set as probabilistic fuzzy rough set (PFRS) on a fuzzy probabilistic approximation space. The proposed PFRS models both vague and uncertain information at the same time. The viability of PFRS in decision making is illustrated through a case study. PFRS is shown to be useful for both probabilistic as well as deterministic problems.
BeauboefTPetryFEAroraG1998Information-theoretic measures of uncertainty for rough sets and rough relational databasesInformation Sciences109185195
2.
BodjanovaS1997Approximation of fuzzy concepts in decision makingFuzzy Sets and Systems8512329
3.
ChunshengFFendingCQiangWShouchaoWJuW2010Application of Rough Sets Theory to Sources Analysis of Atmospheric Particulates4th International Conference on Bioinformatics and Biomedical Engineering (iCBBE)15
4.
DuboisDPradeH1990Rough fuzzy sets and fuzzy rough setsInt J Gen Syst17191209
5.
HuQYuDXieZ2006Information-preserving hybrid data reduction based on fuzzy-rough techniquesPattern Recognit Lett275414423
6.
HuQXieZYuD2007Hybrid attribute reduction based on a novel fuzzy-rough model and information granulationPattern Recog401235093521
7.
HuaJ2008Study on the Application of Rough Sets Theory in Machine LearningIntelligent Information Technology Application, 2008 IITA ’08 Second International Symposium on1192196
8.
JensenRShenQ2004Semantics-preserving dimensionality reduction: Rough and fuzzy-rough based approachesIEEE Trans Knowl Data Eng161214571471
9.
MorsiNNYakoutMM1998Axiomatics for fuzzy rough setsFuzzy Sets and Systems1001-3327342
10.
PadminiSMiguelRVocabulary mining for information retrieval: Rough sets and fuzzy setsInform Process Manage3711538
11.
PawlakZ1982Rough setsInternational Journal of Computer and Information Sciences11341356
12.
RadzikowskaAMKerreEE2002A comparative study of fuzzy rough setsFuzzy Sets Syst126137156
13.
ShiC2009The Application of Rough Sets and Fuzzy Sets in the Supply Chain Knowledge Sharing Risk Early-WarningFuzzy Systems and Knowledge Discovery, 2009 FSKD ’09 Sixth International Conference on6441445
14.
SlezakDZiarkoW2005The investigation of the Bayesian rough set modelInternat J of Approximate Reasoning408191
15.
QinKPeiZ2005On the topological properties of fuzzy rough setsFuzzy Sets Syst1513601613
16.
WalczakBMassartDL1999Rough sets theoryChemometrics and Intelligent Laboratory Systems471116
17.
WangYF2003Mining stock price using fuzzy rough set systemExpert Syst Appl2411323
18.
YaoYY2003Probabilistic approaches to rough setsExpertSystems20287297
19.
YaoYY2010Three-way decisions with probabilistic rough setsInformation Sciences1803341353
20.
YaoYYWongSKMLingrasP1990A decision-theoretic rough set modelMethodologies for Intelligent Systems 5RasZWZemankovaMEmrichML1724North-Holland, New York
21.
YaoYYZhaoY2008Attribute reduction in decision-theoretic rough set modelsInformation Sciences17833563373
22.
ZadehLA1968Probability measures of fuzzy eventsJournal of Mathematical Analysis and Applications23421427
23.
ZhangWXLeungY1996Theory of Including Degrees and its Applications to Uncertainty InferencesSoft Computing in Intelligent Systems and Information Processing, Institute of Electrical and Electronics Engineers496501New York
24.
ZhangQ-FZhaoS-YBaiY-C2009On the application of rough sets to data mining in economic practiceMachine Learning and Cybernetics, 2009 Int Confrence on1272276
25.
ZiarkoW2008Probabilistic approach to rough setsInt Journal of Approx Reasoning49272284
26.
DuboisDPradeH2009Formal representations of uncertainty. In: Decision-making Process- Concepts and MethodsBouyssouDenisDuboisDidierPirlotMarcPradeHenri85156ISTE London & WileyChap. 3
27.
ZiarkoW1993Variable precision rough set modelJ Comput Syst Sci4613959
28.
YaoY2008Probabilistic rough set approximationsInternat J of Approx Reasoning492255271
29.
De CockMCornelisCKerreEE2007Fuzzy Rough Sets: The Forgotten StepIEEE Trans on Fuzzy Systems151121130
30.
YeungDSDegangCTsangECCLeeJWTWangX2005On the generalization of fuzzy rough setsIEEE Trans On Fuzzy Sys133343361
31.
LingrasPJensenR2007Survey of rough and fuzzy hybridization16th Int Conf Fuzzy Syst125130
32.
PolkowskiLSkowronA1996Rough mereology: A new paradigm for approximate reasoningInternational Journal of Approximate Reasoning15333365
33.
ZhangH-YZhangW-X2009Hybrid monotonic inclusion measure and its use in measuring similarity and distance between fuzzy setsFuzzy Sets and Systems1601107118
34.
XuZBLiangJYDangCYChinKS2002Inclusion degree: A perspective on measures for rough set data analysisInformation Sciences141227236
35.
ZadehLA1965Fuzzy sets Inform & Cont83338353
36.
JensenRShenQ2004Fuzzy-rough attributes reduction with application to web categorizationFuzzy Sets and Syst141469485
37.
JensenRShenQ2005Fuzzy-rough data reduction with ant colony optimizationFuzzy Sets & Syst1491520
38.
JensenRShenQ2007Fuzzy-rough sets assisted attribute selectionIEEE Trans on Fuzzy Syst1517389
39.
JensenRShenQ2004Semantics-preserving dimensionality reduction: Rough and fuzzy-rough based approachesIEEE Trans on Knowl & Data Eng161214571471
40.
JensenRShenQ2009New approaches to fuzzy-rough feature selectionIEEE Trans on Fuzzy Syst174824838
41.
Granular computing on binary relations I: Data mining and neighborhood systems in: Rough Sets in Knowledge Discovery, A. Skowron and L. Polkowski, Eds. Berlin, Germany: Physica-Verlag, 1998, pp. 107–121
42.
LinTY1998Granular computing on binary relations II: Rough set representations and belief functions in: Rough Sets in Knowledge DiscoverySkowronAPolkowskiL122140Berlin, GermanyPhysica-Verlag
43.
LingrasP2001Fuzzy-rough and rough-fuzzy serial combinations in neurocomputingNeurocomput361–42944
44.
SarkarM2001Measures of ruggedness using fuzzy-rough sets and fractals: Applications in medical time seriesIEEE Int Conf Syst, Man, and Cyb315141519
45.
PalSKMitraP2004Case generation using rough sets with fuzzy representationIEEE Trans Knowl Data Eng163292300
46.
WangY-F2005Mining stock price using fuzzy rough set systemExp Syst Appl
47.
LiuDLiTZhangJ2015Incremental updating approximations in probabilistic rough sets under the variation of attributesKnowledge-Based Systems738196
48.
WangGMaXYuH2015Monotonic uncertainty measures for attribute reduction in probabilistic rough set modelInternational Journal of Approximate Reasoning(in press)
49.
ZiarkoW2008Probabilistic approach to rough setsInternational Journal of Approximate Reasoning492272284
50.
LiT-JYangX-P2014An axiomatic characterization of probabilistic rough setsInternational Journal of Approximate Reasoning551130141Part 2
51.
XuZBLiangJYDangCYChinKS2002Inclusion degree: A perspective on measures for rough set data analysisInform Sci141227236
52.
ZhangMXuLDZhangWXLiHZ2003A rough set approach to knowledge reduction based on inclusion degree and evidence reasoning theoryExpert Syst20298304
53.
ZhangWXLeungY1996The Uncertainty Reasoning Principles (in Chinese), Xi’an Jiaotong University Press, Xi’anChina
54.
ZhangWXLeungY1996Theory of including degrees and its applications to uncertainty inferencesProceedings of the 1996 Asian Fuzzy Systems Symposium, Soft Computing in Intelligent Syst and Inform Processing496501
SkowronAPolkowskiL1998Rough mereological foundations for design, analysis, synthesis, and control in distributed systemsInform Sci104129156
57.
GrecoSMatarazzoBSłowinśkiR2005Rough membership and Bayesian confirmation measures for parameterized rough setsProceedings of the 10th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, RSFDGrC 2005, LNCS (LNAI)3641314324
58.
GrecoSSłowinskiRSzczechI2008Assessing the quality of rules with a new monotonic interestingness measure ZProceedings of the 9th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2008, LNCS (LNAI)5097556565
59.
Yao anYDengX2014Quantitative rough sets based on subsethood measuresInformation Sciences267306322
