Fuzzy probabilistic rough sets and their corresponding three-way decisions

The concept of probabilistic rough sets, as a main subject of this paper, is intimately connected with the concept of decision-theoretic rough sets. This paper investigates fuzzy and interval-valued fuzzy probabilistic rough sets within frameworks of fuzzy and interval-valued fuzzy probabilistic app...

Full description

Saved in:
Bibliographic Details
Published inKnowledge-based systems Vol. 91; pp. 126 - 142
Main Authors Zhao, Xue Rong, Hu, Bao Qing
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.01.2016
Subjects
Fuzzy event
Fuzzy probabilistic rough set
Interval-valued fuzzy event
Interval-valued fuzzy probabilistic rough set
Rough set
Three-way decisions
Three-way decisions
Interval-valued fuzzy probabilistic rough set
Fuzzy probabilistic rough set
Fuzzy event
Interval-valued fuzzy event
Rough set
Online AccessGet full text

Cover

Abstract The concept of probabilistic rough sets, as a main subject of this paper, is intimately connected with the concept of decision-theoretic rough sets. This paper investigates fuzzy and interval-valued fuzzy probabilistic rough sets within frameworks of fuzzy and interval-valued fuzzy probabilistic approximation spaces, respectively. Four types of fuzzy probabilistic rough sets as well as interval-valued fuzzy probabilistic rough sets are established in terms of different constraints on parameters. To find a suitable way of explaining and determining these parameters in each model, three-way decisions are studied based on Bayesian minimum risk decision procedure, i.e., the decision-theoretic rough set approach. The proposed models in this paper broaden applications of probabilistic rough sets due to their abilities of directly dealing with real-valued and interval-valued data.
AbstractList The concept of probabilistic rough sets, as a main subject of this paper, is intimately connected with the concept of decision-theoretic rough sets. This paper investigates fuzzy and interval-valued fuzzy probabilistic rough sets within frameworks of fuzzy and interval-valued fuzzy probabilistic approximation spaces, respectively. Four types of fuzzy probabilistic rough sets as well as interval-valued fuzzy probabilistic rough sets are established in terms of different constraints on parameters. To find a suitable way of explaining and determining these parameters in each model, three-way decisions are studied based on Bayesian minimum risk decision procedure, i.e., the decision-theoretic rough set approach. The proposed models in this paper broaden applications of probabilistic rough sets due to their abilities of directly dealing with real-valued and interval-valued data.
Author Hu, Bao Qing
Zhao, Xue Rong
Author_xml – sequence: 1
  givenname: Xue Rong
  surname: Zhao
  fullname: Zhao, Xue Rong
  organization: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China
– sequence: 2
  givenname: Bao Qing
  orcidid: 0000-0002-3861-4652
  surname: Hu
  fullname: Hu, Bao Qing
  email: bqhu@whu.edu.cn, bqhujjhe@hotmail.com
  organization: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China
BookMark eNqFkMtOwzAQRS1UJNrCH7DIDySMkzROWCChivIQEhtYW85k0roUu7JdUPr1uCorFrCa0Ujn6s6ZsJGxhhi75JBx4NXVOns31g8-y4HPMmgy4PUJG_Na5KkooRmxMTQzSAXM-BmbeL8GgDzn9Zg9LXb7_ZBsnW1VqzfaB42Js7vlKvEUfKJMl4QVaZegdY781ppOm2W8OaL0Sw1JR6i9tsafs9NebTxd_Mwpe1vcvc4f0ueX-8f57XOKBVQhxR6wUk1VtgWpEoWAvBIdqbpqERXmdckL6EtBsbjohYo9G2iLNu-xVl3cpqw85qKz3jvq5dbpD-UGyUEefMi1PPqQBx8SGhl9ROz6F4Y6qBCbB6f05j_45ghTfOxTk5MeNRmkTjvCIDur_w74Bgj2gzA
CitedBy_id crossref_primary_10_1016_j_ijar_2018_09_005
crossref_primary_10_3233_JIFS_221424
crossref_primary_10_3233_JIFS_17888
crossref_primary_10_1016_j_knosys_2017_10_003
crossref_primary_10_1016_j_ins_2023_119962
crossref_primary_10_1016_j_knosys_2018_01_008
crossref_primary_10_1007_s13042_020_01082_x
crossref_primary_10_1016_j_future_2019_07_049
crossref_primary_10_1016_j_knosys_2017_03_013
crossref_primary_10_1057_s41274_016_0159_2
crossref_primary_10_1007_s13042_019_01040_2
crossref_primary_10_1007_s00500_020_05283_y
crossref_primary_10_1007_s10489_020_02142_z
crossref_primary_10_1007_s10489_021_02673_z
crossref_primary_10_1016_j_ins_2023_119365
crossref_primary_10_1007_s00500_023_09427_8
crossref_primary_10_1007_s10489_023_05085_3
crossref_primary_10_1007_s10462_022_10316_z
crossref_primary_10_1016_j_ins_2018_07_032
crossref_primary_10_1155_2017_1608147
crossref_primary_10_3233_IFS_162200
crossref_primary_10_1007_s12559_016_9397_5
crossref_primary_10_1016_j_knosys_2016_01_036
crossref_primary_10_1016_j_ins_2019_05_022
crossref_primary_10_1007_s41066_018_0111_8
crossref_primary_10_1016_j_asoc_2023_111066
crossref_primary_10_3233_IFS_162204
crossref_primary_10_1016_j_ijar_2018_11_014
crossref_primary_10_1016_j_ijar_2016_12_007
crossref_primary_10_1007_s13042_016_0568_1
crossref_primary_10_1016_j_ijar_2022_03_009
crossref_primary_10_1016_j_ins_2019_06_064
crossref_primary_10_1007_s00500_019_04038_8
crossref_primary_10_1016_j_ins_2018_03_049
crossref_primary_10_1016_j_ins_2019_09_037
crossref_primary_10_1016_j_ijar_2017_07_012
crossref_primary_10_1007_s40747_018_0090_z
crossref_primary_10_1016_j_knosys_2022_109522
crossref_primary_10_1109_TFUZZ_2016_2632745
crossref_primary_10_1016_j_knosys_2018_07_008
crossref_primary_10_1016_j_ijar_2019_11_002
crossref_primary_10_1002_cjce_23159
crossref_primary_10_1016_j_ins_2017_12_005
crossref_primary_10_1016_j_ins_2018_08_024
crossref_primary_10_1016_j_cogsys_2020_05_001
crossref_primary_10_1007_s13042_016_0591_2
crossref_primary_10_1016_j_knosys_2016_04_002
crossref_primary_10_1016_j_ins_2023_119912
crossref_primary_10_1016_j_ijar_2017_01_005
crossref_primary_10_1109_TFUZZ_2019_2955047
crossref_primary_10_1007_s41066_018_0090_9
crossref_primary_10_1016_j_asoc_2023_110144
crossref_primary_10_1016_j_ins_2019_06_003
crossref_primary_10_1016_j_ijar_2017_11_015
crossref_primary_10_1016_j_ins_2016_12_012
crossref_primary_10_1007_s00500_017_2765_6
crossref_primary_10_1007_s13042_019_01013_5
crossref_primary_10_1016_j_ijar_2017_08_004
crossref_primary_10_1016_j_ins_2020_10_043
Cites_doi 10.1016/j.ins.2014.04.022
10.1016/j.ins.2009.09.021
10.1016/j.ins.2008.05.010
10.1007/BF01001956
10.1007/3-540-39205-X_46
10.1016/S0020-7373(88)80032-4
10.1007/978-3-642-16248-0_97
10.1142/S0218488512400090
10.1007/978-3-642-24425-4_65
10.1016/j.ijar.2007.05.019
10.1016/j.ijar.2011.12.010
10.1016/0022-247X(68)90078-4
10.1080/03081079.2011.634067
10.1007/978-3-642-18859-6_19
10.1016/j.ins.2010.11.019
10.1007/978-3-642-02962-2_81
10.1016/j.ijar.2013.02.012
10.1016/0020-7373(92)90069-W
10.1016/j.knosys.2013.03.012
10.1016/j.ijar.2007.06.014
10.3233/FI-2011-423
10.1007/978-3-540-73451-2_38
10.1016/j.ins.2014.06.045
10.3934/jimo.2006.2.351
10.1016/j.ijar.2013.05.001
10.1080/18756891.2011.9727764
10.1016/j.ins.2014.05.015
10.1007/978-3-540-79721-0_90
10.1016/j.ins.2014.12.008
10.1007/11548669_31
10.1007/978-3-540-74976-9_18
10.1016/0022-0000(93)90048-2
10.1109/TKDE.2008.236
10.1016/S0950-7051(00)00088-5
10.1016/S1571-0661(04)80724-2
10.1007/978-3-642-13059-5_6
10.1007/978-3-642-32115-3_34
10.1016/j.ins.2014.02.054
10.1007/978-3-540-72458-2_1
10.1016/j.ins.2014.10.046
10.1016/j.ijar.2013.03.014
10.1109/TFUZZ.2012.2235839
10.1016/j.ijar.2004.11.004
10.1016/0165-0114(86)90077-1
10.1016/j.csda.2011.06.036
10.1080/03081079.2015.1028540
10.1016/0165-0114(96)84611-2
10.1016/0165-0114(87)90135-7
10.1016/S0019-9958(65)90241-X
10.1007/11548669_30
10.1016/j.ijar.2011.12.006
ContentType Journal Article
Copyright 2015 Elsevier B.V.
Copyright_xml – notice: 2015 Elsevier B.V.
DBID AAYXX
CITATION
DOI 10.1016/j.knosys.2015.09.018
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
EISSN 1872-7409
EndPage 142
ExternalDocumentID 10_1016_j_knosys_2015_09_018
S0950705115003573
GroupedDBID --K
--M
.DC
.~1
0R~
1B1
1~.
1~5
29L
4.4
457
4G.
5VS
7-5
71M
77K
8P~
9JN
AACTN
AAEDT
AAEDW
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AAXUO
AAYFN
ABAOU
ABBOA
ABIVO
ABJNI
ABMAC
ABXDB
ABYKQ
ACAZW
ACDAQ
ACGFS
ACNNM
ACRLP
ACZNC
ADBBV
ADEZE
ADGUI
ADJOM
ADMUD
ADTZH
AEBSH
AECPX
AEKER
AENEX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHJVU
AHZHX
AIALX
AIEXJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
AOUOD
ARUGR
ASPBG
AVWKF
AXJTR
AZFZN
BJAXD
BKOJK
BLXMC
CS3
DU5
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
G8K
GBLVA
GBOLZ
HLZ
HVGLF
HZ~
IHE
J1W
JJJVA
KOM
LG9
LY7
M41
MHUIS
MO0
N9A
O-L
O9-
OAUVE
OZT
P-8
P-9
P2P
PC.
PQQKQ
Q38
R2-
RIG
ROL
RPZ
SBC
SDF
SDG
SDP
SES
SET
SEW
SPC
SPCBC
SST
SSV
SSW
SSZ
T5K
UHS
WH7
WUQ
XPP
ZMT
~02
~G-
AATTM
AAXKI
AAYWO
AAYXX
ABDPE
ABWVN
ACRPL
ACVFH
ADCNI
ADNMO
AEIPS
AEUPX
AFJKZ
AFPUW
AFXIZ
AGCQF
AGQPQ
AGRNS
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
BNPGV
CITATION
SSH
ID FETCH-LOGICAL-c306t-cf0c6a964b3ea4c770267dea86bccac284130f47e4097f7a22190b3b2fc8ad0b3
IEDL.DBID .~1
ISSN 0950-7051
IngestDate Thu Apr 24 23:08:00 EDT 2025
Tue Jul 01 04:37:46 EDT 2025
Fri Feb 23 02:28:21 EST 2024
IsPeerReviewed true
IsScholarly true
Keywords Three-way decisions
Interval-valued fuzzy probabilistic rough set
Fuzzy probabilistic rough set
Fuzzy event
Interval-valued fuzzy event
Rough set
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c306t-cf0c6a964b3ea4c770267dea86bccac284130f47e4097f7a22190b3b2fc8ad0b3
ORCID 0000-0002-3861-4652
PageCount 17
ParticipantIDs crossref_primary_10_1016_j_knosys_2015_09_018
crossref_citationtrail_10_1016_j_knosys_2015_09_018
elsevier_sciencedirect_doi_10_1016_j_knosys_2015_09_018
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate January 2016
2016-01-00
PublicationDateYYYYMMDD 2016-01-01
PublicationDate_xml – month: 01
  year: 2016
  text: January 2016
PublicationDecade 2010
PublicationTitle Knowledge-based systems
PublicationYear 2016
Publisher Elsevier B.V
Publisher_xml – name: Elsevier B.V
References Hu (bib0011) 2014; 281
Ziarko (bib0068) 2008; 49
Liu, Yao, Li (bib0030) 2011; 4
Yao (bib0052) 2011; 181
Duda, Hart (bib0008) 1973
Lingras, Chen, Miao (bib0027) 2009; 21
Zhao, Hu (bib0062) 2015; 298
Ziarko (bib0066) 2003; 82
Liu, Liang, Wang (bib0029) 2015
Yao (bib0051) 2010; 180
Pawlak (bib0035) 1982; 11
Li, Zhang, Huang, Zhou (bib0022) 2015
Klir, Yuan (bib0019) 1995
Li, Zhang, Swan (bib0023) 2000; 13
Sang, Liang, Qian (bib0038) 2015
Herbert, Yao (bib0010) 2011; 108
Pawlak, Wong, Ziarko (bib0037) 1988; 29
Bobadilla, Ortega, Hernando, Gutiérrez (bib0003) 2013; 46
Hu, Wong (bib0015) 2013; 15
Sun, Ma, Zhao (bib0042) 2014; 283
B.Q. Hu, Three-way decision spaces based on partially ordered sets and three-way decisions based on hesitant fuzzy sets, Knowl.-Based Syst.
Liu, Li, Liang (bib0028) 2012; 20
Zhou, Yao, Luo (bib0063) 2010; 6085
Lingras, Chen, Miao (bib0026) 2008; 5009
van den Berg, Kaymak, Almeida (bib0002) 2013; 21
Katzberg, Ziarko (bib0018) 1994
Ma, Sun (bib0031) 2012; 41
Ziarko (bib0067) 2005; 3641
Deng, Yao (bib0007) 2014; 279
Ślȩzak, Ziarko (bib0039) 2002
.
Yang, Liao, Wang, Wang (bib0057) 2013; 54
Gut (bib0009) 2013
Yao (bib0047) 2004
Yao, Greco, Słowiński (bib0053) 2015
Hu (bib0013) 2015; 44
Burillo, Bustince (bib0004) 1996; 78
Dembczyński, Greco, Kotłowski, Słowiński (bib0006) 2007; 4702
Nishino, Nagamachi, Tanaka (bib0034) 2005; 3641
Capotorti, Barbanera (bib0005) 2012; 56
Zhang, Zhou, Miao, Gao (bib0061) 2012; 53
Hu, Wong (bib0016) 2014; 16
Li, Yang (bib0021) 2014; 55
Yao, Wong (bib0046) 1992; 37
Yao, Zhao (bib0055) 2008; 178
Azam, Yao (bib0001) 2015; 295
Wong, Ziarko (bib0044) 1987; 21
Yao, Herbert (bib0054) 2007; 4585
Yao (bib0048) 2007; 4481
Ślȩzak, Ziarko (bib0041) 2005; 40
Ziarko (bib0064) 1993; 46
Ziarko (bib0065) 2002; 87
Turksen (bib0043) 1986; 20
Jia, Zheng, Li, Liu, Shang (bib0017) 2012; 7413
Yao, Wong, Lingras (bib0045) 1990
Yao, Zhou (bib0056) 2010; 6401
Liang, Liu, Pedrycz, Hu (bib0025) 2013; 54
Pawlak (bib0036) 1991
Yao (bib0050) 2009; 5589
Ma, Sun (bib0032) 2012; 53
Ślȩzak, Ziarko (bib0040) 2003; 2639
Yao (bib0049) 2008; 49
Zadeh (bib0060) 1968; 23
Hu, Wang (bib0014) 2006; 2
Zadeh (bib0059) 1965; 8
Moore (bib0033) 1966
Li, Miao, Wang, Zhang (bib0020) 2010
Liang, Liu (bib0024) 2014; 276
Yu, Liu, Wang (bib0058) 2011; 6954
Yao (10.1016/j.knosys.2015.09.018_bib0054) 2007; 4585
Sun (10.1016/j.knosys.2015.09.018_bib0042) 2014; 283
Li (10.1016/j.knosys.2015.09.018_bib0023) 2000; 13
Nishino (10.1016/j.knosys.2015.09.018_bib0034) 2005; 3641
Yao (10.1016/j.knosys.2015.09.018_bib0056) 2010; 6401
Li (10.1016/j.knosys.2015.09.018_bib0022) 2015
Ziarko (10.1016/j.knosys.2015.09.018_bib0066) 2003; 82
Pawlak (10.1016/j.knosys.2015.09.018_bib0036) 1991
Ziarko (10.1016/j.knosys.2015.09.018_bib0068) 2008; 49
Hu (10.1016/j.knosys.2015.09.018_bib0011) 2014; 281
Sang (10.1016/j.knosys.2015.09.018_bib0038) 2015
Ślȩzak (10.1016/j.knosys.2015.09.018_bib0039) 2002
Azam (10.1016/j.knosys.2015.09.018_bib0001) 2015; 295
Dembczyński (10.1016/j.knosys.2015.09.018_bib0006) 2007; 4702
Liang (10.1016/j.knosys.2015.09.018_bib0025) 2013; 54
Ślȩzak (10.1016/j.knosys.2015.09.018_bib0040) 2003; 2639
Gut (10.1016/j.knosys.2015.09.018_bib0009) 2013
Yao (10.1016/j.knosys.2015.09.018_bib0045) 1990
Yang (10.1016/j.knosys.2015.09.018_bib0057) 2013; 54
Li (10.1016/j.knosys.2015.09.018_bib0021) 2014; 55
Liu (10.1016/j.knosys.2015.09.018_bib0029) 2015
Liu (10.1016/j.knosys.2015.09.018_bib0030) 2011; 4
10.1016/j.knosys.2015.09.018_bib0012
Yao (10.1016/j.knosys.2015.09.018_bib0050) 2009; 5589
Yao (10.1016/j.knosys.2015.09.018_bib0052) 2011; 181
Hu (10.1016/j.knosys.2015.09.018_bib0013) 2015; 44
Lingras (10.1016/j.knosys.2015.09.018_bib0027) 2009; 21
Capotorti (10.1016/j.knosys.2015.09.018_bib0005) 2012; 56
Pawlak (10.1016/j.knosys.2015.09.018_bib0037) 1988; 29
Ma (10.1016/j.knosys.2015.09.018_bib0032) 2012; 53
Yu (10.1016/j.knosys.2015.09.018_bib0058) 2011; 6954
Hu (10.1016/j.knosys.2015.09.018_bib0016) 2014; 16
Liang (10.1016/j.knosys.2015.09.018_bib0024) 2014; 276
Lingras (10.1016/j.knosys.2015.09.018_bib0026) 2008; 5009
Zhou (10.1016/j.knosys.2015.09.018_bib0063) 2010; 6085
Ziarko (10.1016/j.knosys.2015.09.018_bib0067) 2005; 3641
Zhao (10.1016/j.knosys.2015.09.018_bib0062) 2015; 298
Deng (10.1016/j.knosys.2015.09.018_bib0007) 2014; 279
Turksen (10.1016/j.knosys.2015.09.018_bib0043) 1986; 20
Zhang (10.1016/j.knosys.2015.09.018_bib0061) 2012; 53
Yao (10.1016/j.knosys.2015.09.018_bib0047) 2004
Li (10.1016/j.knosys.2015.09.018_bib0020) 2010
Zadeh (10.1016/j.knosys.2015.09.018_bib0060) 1968; 23
Ziarko (10.1016/j.knosys.2015.09.018_bib0064) 1993; 46
Hu (10.1016/j.knosys.2015.09.018_bib0014) 2006; 2
Duda (10.1016/j.knosys.2015.09.018_bib0008) 1973
Wong (10.1016/j.knosys.2015.09.018_bib0044) 1987; 21
Bobadilla (10.1016/j.knosys.2015.09.018_bib0003) 2013; 46
Yao (10.1016/j.knosys.2015.09.018_bib0051) 2010; 180
Yao (10.1016/j.knosys.2015.09.018_bib0049) 2008; 49
Katzberg (10.1016/j.knosys.2015.09.018_bib0018) 1994
Ma (10.1016/j.knosys.2015.09.018_bib0031) 2012; 41
Burillo (10.1016/j.knosys.2015.09.018_bib0004) 1996; 78
Jia (10.1016/j.knosys.2015.09.018_bib0017) 2012; 7413
Yao (10.1016/j.knosys.2015.09.018_bib0055) 2008; 178
Liu (10.1016/j.knosys.2015.09.018_bib0028) 2012; 20
Zadeh (10.1016/j.knosys.2015.09.018_bib0059) 1965; 8
Herbert (10.1016/j.knosys.2015.09.018_bib0010) 2011; 108
Pawlak (10.1016/j.knosys.2015.09.018_bib0035) 1982; 11
Yao (10.1016/j.knosys.2015.09.018_bib0046) 1992; 37
Yao (10.1016/j.knosys.2015.09.018_bib0053) 2015
Yao (10.1016/j.knosys.2015.09.018_bib0048) 2007; 4481
Ziarko (10.1016/j.knosys.2015.09.018_bib0065) 2002; 87
Klir (10.1016/j.knosys.2015.09.018_bib0019) 1995
Ślȩzak (10.1016/j.knosys.2015.09.018_bib0041) 2005; 40
Hu (10.1016/j.knosys.2015.09.018_bib0015) 2013; 15
van den Berg (10.1016/j.knosys.2015.09.018_bib0002) 2013; 21
Moore (10.1016/j.knosys.2015.09.018_bib0033) 1966
References_xml – volume: 13
  start-page: 285
  year: 2000
  end-page: 296
  ident: bib0023
  article-title: An information filtering model on the Web and its application in JobAgent
  publication-title: Knowl.-Based Syst.
– volume: 21
  start-page: 357
  year: 1987
  end-page: 362
  ident: bib0044
  article-title: Comparison of the probabilistic approximate classification and the fuzzy set model
  publication-title: Fuzzy Sets Syst.
– volume: 108
  start-page: 267
  year: 2011
  end-page: 286
  ident: bib0010
  article-title: Game-theoretic rough sets
  publication-title: Fundam. Inf.
– year: 2013
  ident: bib0009
  publication-title: Probability: A Graduate Course
– volume: 283
  start-page: 180
  year: 2014
  end-page: 196
  ident: bib0042
  article-title: Decision-theoretic rough fuzzy set model and application
  publication-title: Inf. Sci.
– volume: 53
  start-page: 541
  year: 2012
  end-page: 557
  ident: bib0061
  article-title: Bayesian rough set model: a further investigation
  publication-title: Int. J. Approx. Reason.
– volume: 55
  start-page: 130
  year: 2014
  end-page: 141
  ident: bib0021
  article-title: An axiomatic characterization of probabilistic rough sets
  publication-title: Int. J. Approx. Reason.
– volume: 82
  start-page: 263
  year: 2003
  end-page: 273
  ident: bib0066
  article-title: Attribute reduction in the Bayesian version of variable precision rough set model
  publication-title: Electron. Notes Theor. Comput. Sci.
– volume: 178
  start-page: 3356
  year: 2008
  end-page: 3373
  ident: bib0055
  article-title: Attribute reduction in decision-theoretic rough set models
  publication-title: Inf. Sci.
– volume: 4702
  start-page: 164
  year: 2007
  end-page: 175
  ident: bib0006
  article-title: Statistical model for rough set approach to multicriteria classification
  publication-title: Lect. Notes Comput. Sci.
– volume: 4
  start-page: 66
  year: 2011
  end-page: 74
  ident: bib0030
  article-title: Three-way investment decisions with decision-theoretic rough sets
  publication-title: Int. J. Comput. Intell. Syst.
– volume: 7413
  start-page: 287
  year: 2012
  end-page: 296
  ident: bib0017
  article-title: Three-way decisions solution to filter spam email: an empirical study
  publication-title: Lect. Notes Comput. Sci.
– volume: 20
  start-page: 191
  year: 1986
  end-page: 210
  ident: bib0043
  article-title: Interval valued fuzzy sets based on normal forms
  publication-title: Fuzzy Sets Syst.
– year: 2015
  ident: bib0038
  article-title: Decision-theoretic rough sets under dynamic granulation
  publication-title: Knowl.-Based Syst.
– start-page: 484
  year: 2010
  end-page: 489
  ident: bib0020
  article-title: Hierarchical rough decision theoretic framework for text classification
  publication-title: 2010 9th IEEE International Conference on Cognitive Informatics (ICCI)
– volume: 276
  start-page: 186
  year: 2014
  end-page: 203
  ident: bib0024
  article-title: Systematic studies on three-way decisions with interval-valued decision-theoretic rough sets
  publication-title: Inf. Sci.
– volume: 181
  start-page: 1080
  year: 2011
  end-page: 1096
  ident: bib0052
  article-title: The superiority of three-way decisions in probabilistic rough set models
  publication-title: Inf. Sci.
– volume: 21
  start-page: 1014
  year: 2009
  end-page: 1026
  ident: bib0027
  article-title: Rough cluster quality index based on decision theory
  publication-title: IEEE Trans. Knowl. Data Eng.
– volume: 46
  start-page: 109
  year: 2013
  end-page: 132
  ident: bib0003
  article-title: Recommender systems survey
  publication-title: Knowl.-Based Syst.
– volume: 53
  start-page: 608
  year: 2012
  end-page: 619
  ident: bib0032
  article-title: Probabilistic rough set over two universes and rough entropy
  publication-title: Int. J. Approx. Reason.
– volume: 78
  start-page: 305
  year: 1996
  end-page: 316
  ident: bib0004
  article-title: Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets
  publication-title: Fuzzy Sets Syst.
– volume: 41
  start-page: 225
  year: 2012
  end-page: 245
  ident: bib0031
  article-title: On relationship between probabilistic rough set and Bayesian risk decision over two universes
  publication-title: Int. J. Gen. Syst.
– volume: 281
  start-page: 21
  year: 2014
  end-page: 52
  ident: bib0011
  article-title: Three-way decisions space and three-way decisions
  publication-title: Inf. Sci.
– year: 2015
  ident: bib0022
  article-title: Sequential three-way decision and granulation for cost-sensitive face recognition
  publication-title: Knowl.-Based Syst.
– volume: 54
  start-page: 1087
  year: 2013
  end-page: 1106
  ident: bib0025
  article-title: Triangular fuzzy decision-theoretic rough sets
  publication-title: Int. J. Approx. Reason.
– start-page: 167
  year: 1994
  end-page: 177
  ident: bib0018
  article-title: Variable precision rough sets with asymmetric bounds
  publication-title: Rough Sets, Fuzzy Sets and Knowledge Discovery
– volume: 29
  start-page: 81
  year: 1988
  end-page: 95
  ident: bib0037
  article-title: Rough sets: probabilistic versus deterministic approach
  publication-title: Int. J. Man-Mach. Stud.
– volume: 279
  start-page: 702
  year: 2014
  end-page: 715
  ident: bib0007
  article-title: Decision-theoretic three-way approximations of fuzzy sets
  publication-title: Inf. Sci.
– volume: 2639
  start-page: 312
  year: 2003
  end-page: 315
  ident: bib0040
  article-title: Variable precision Bayesian rough set model
  publication-title: Lect. Notes Comput. Sci.
– volume: 16
  start-page: 554
  year: 2014
  end-page: 565
  ident: bib0016
  article-title: Generalized interval-valued fuzzy variable precision rough sets
  publication-title: Int. J. Fuzzy Syst.
– volume: 37
  start-page: 793
  year: 1992
  end-page: 809
  ident: bib0046
  article-title: A decision theoretic framework for approximating concepts
  publication-title: Int. J. Man-Mach. Stud.
– volume: 11
  start-page: 341
  year: 1982
  end-page: 356
  ident: bib0035
  article-title: Rough set
  publication-title: Int. J. Comput. Inf. Sci.
– year: 2015
  ident: bib0029
  article-title: A novel three-way decision model based on incomplete information system
  publication-title: Knowl.-Based Syst.
– reference: B.Q. Hu, Three-way decision spaces based on partially ordered sets and three-way decisions based on hesitant fuzzy sets, Knowl.-Based Syst.,
– start-page: 17
  year: 1990
  end-page: 24
  ident: bib0045
  article-title: A decision-theoretic rough set model
  publication-title: Methodologies for Intelligent System
– volume: 4481
  start-page: 1
  year: 2007
  end-page: 12
  ident: bib0048
  article-title: Decision-theoretic rough set models
  publication-title: Lect. Notes Comput. Sci.
– volume: 4585
  start-page: 360
  year: 2007
  end-page: 370
  ident: bib0054
  article-title: Web-based support systems with rough set analysis
  publication-title: Lect. Notes Comput. Sci.
– start-page: 387
  year: 2015
  end-page: 411
  ident: bib0053
  article-title: Probabilistic rough sets
  publication-title: Handbook of Computational Intelligence
– volume: 20
  start-page: 119
  year: 2012
  end-page: 132
  ident: bib0028
  article-title: Three-way government decision analysis with decision-theoretic rough sets
  publication-title: Int. J. Uncertain. Fuzziness Knowl.-Based Syst.
– volume: 2
  start-page: 351
  year: 2006
  end-page: 371
  ident: bib0014
  article-title: A novel approach in uncertain programming part I: new arithmetic and order relation for interval numbers
  publication-title: J. Ind. Manage. Optim.
– volume: 54
  start-page: 1410
  year: 2013
  end-page: 1420
  ident: bib0057
  article-title: Fuzzy probabilistic rough set model on two universes and its applications
  publication-title: Int. J. Approx. Reason.
– volume: 40
  start-page: 81
  year: 2005
  end-page: 91
  ident: bib0041
  article-title: The investigation of the Bayesian rough set model
  publication-title: Int. J. Approx. Reason.
– volume: 180
  start-page: 341
  year: 2010
  end-page: 353
  ident: bib0051
  article-title: Three-way decisions with probabilistic rough sets
  publication-title: Inf. Sci.
– volume: 5589
  start-page: 642
  year: 2009
  end-page: 649
  ident: bib0050
  article-title: Three-way decision: an interpretation of rules in rough set theory
  publication-title: Lect. Notes Comput. Sci.
– volume: 295
  start-page: 586
  year: 2015
  end-page: 599
  ident: bib0001
  article-title: Interpretation of equilibria in game-theoretic rough sets
  publication-title: Inf. Sci.
– volume: 6401
  start-page: 719
  year: 2010
  end-page: 726
  ident: bib0056
  article-title: Naive Bayesian rough sets
  publication-title: Lect. Notes Comput. Sci.
– year: 1966
  ident: bib0033
  publication-title: Interval Analysis
– volume: 46
  start-page: 39
  year: 1993
  end-page: 59
  ident: bib0064
  article-title: Variable precision rough set model
  publication-title: J. Comput. Syst. Sci.
– year: 1973
  ident: bib0008
  publication-title: Pattern Classification and Scene Analysis
– volume: 44
  start-page: 849
  year: 2015
  end-page: 875
  ident: bib0013
  article-title: Generalized interval-valued fuzzy variable precision rough sets determined by fuzzy logical operators
  publication-title: Int. J. Gen. Syst.
– volume: 3641
  start-page: 294
  year: 2005
  end-page: 303
  ident: bib0034
  article-title: Variable precision Bayesian rough set model and its application to human evaluation data
  publication-title: Lect. Notes Comput. Sci.
– volume: 8
  start-page: 338
  year: 1965
  end-page: 358
  ident: bib0059
  article-title: Fuzzy sets
  publication-title: Inf. Control
– year: 1995
  ident: bib0019
  publication-title: Fuzzy Sets and Fuzzy Logic
– volume: 56
  start-page: 981
  year: 2012
  end-page: 994
  ident: bib0005
  article-title: Credit scoring analysis using a fuzzy probabilistic rough set model
  publication-title: Comput. Stat. Data Anal.
– volume: 6954
  start-page: 504
  year: 2011
  end-page: 513
  ident: bib0058
  article-title: Automatically determining the number of clusters using decision-theoretic rough set
  publication-title: Lect. Notes Comput. Sci.
– volume: 21
  start-page: 869
  year: 2013
  end-page: 882
  ident: bib0002
  article-title: Conditional density estimation using probabilistic fuzzy systems
  publication-title: IEEE Trans. Fuzzy Syst.
– volume: 49
  start-page: 272
  year: 2008
  end-page: 284
  ident: bib0068
  article-title: Probabilistic approach to rough sets
  publication-title: Int. J. Approx. Reason.
– volume: 87
  start-page: 442
  year: 2002
  end-page: 452
  ident: bib0065
  article-title: Set approximation quality measures in the variable precision rough set model, in: Proceedings of the 2nd International Conference on Hybrid Intelligent Systems (HIS’02)
– volume: 298
  start-page: 534
  year: 2015
  end-page: 554
  ident: bib0062
  article-title: Fuzzy and interval-valued fuzzy decision-theoretic rough set approaches based on the fuzzy probability measure
  publication-title: Inf. Sci.
– start-page: 491
  year: 2004
  end-page: 516
  ident: bib0047
  article-title: Information granulation and approximation in a decision-theoretical model of rough sets
  publication-title: Cognit. Technol.
– start-page: 131
  year: 2002
  end-page: 135
  ident: bib0039
  article-title: Bayesian rough set model
  publication-title: Proceedings of the International Workshop on Foundation of Data Mining (FDM’2002), December 9, Maebashi, Japan
– year: 1991
  ident: bib0036
  publication-title: Rough Set: Theoretical Aspects of Reasoning About Data
– volume: 15
  start-page: 381
  year: 2013
  end-page: 391
  ident: bib0015
  article-title: Generalized interval-valued fuzzy rough sets based on interval-valued fuzzy logical operators
  publication-title: Int. J. Fuzzy Syst.
– volume: 49
  start-page: 255
  year: 2008
  end-page: 271
  ident: bib0049
  article-title: Probabilistic rough set approximations
  publication-title: Int. J. Approx. Reason.
– volume: 3641
  start-page: 283
  year: 2005
  end-page: 293
  ident: bib0067
  article-title: Probabilistic rough sets
  publication-title: Lect. Notes Comput. Sci.
– volume: 23
  start-page: 421
  year: 1968
  end-page: 427
  ident: bib0060
  article-title: Probability measures of fuzzy events
  publication-title: J. Math. Anal. Appl.
– reference: .
– volume: 5009
  start-page: 676
  year: 2008
  end-page: 683
  ident: bib0026
  article-title: Rough multi-category decision theoretic framework
  publication-title: Lect. Notes Comput. Sci.
– volume: 6085
  start-page: 28
  year: 2010
  end-page: 39
  ident: bib0063
  article-title: A three-way decision approach to email spam filtering
  publication-title: Lect. Notes Comput. Sci.
– volume: 15
  start-page: 381
  year: 2013
  ident: 10.1016/j.knosys.2015.09.018_bib0015
  article-title: Generalized interval-valued fuzzy rough sets based on interval-valued fuzzy logical operators
  publication-title: Int. J. Fuzzy Syst.
– volume: 279
  start-page: 702
  year: 2014
  ident: 10.1016/j.knosys.2015.09.018_bib0007
  article-title: Decision-theoretic three-way approximations of fuzzy sets
  publication-title: Inf. Sci.
  doi: 10.1016/j.ins.2014.04.022
– volume: 180
  start-page: 341
  year: 2010
  ident: 10.1016/j.knosys.2015.09.018_bib0051
  article-title: Three-way decisions with probabilistic rough sets
  publication-title: Inf. Sci.
  doi: 10.1016/j.ins.2009.09.021
– volume: 178
  start-page: 3356
  year: 2008
  ident: 10.1016/j.knosys.2015.09.018_bib0055
  article-title: Attribute reduction in decision-theoretic rough set models
  publication-title: Inf. Sci.
  doi: 10.1016/j.ins.2008.05.010
– volume: 11
  start-page: 341
  year: 1982
  ident: 10.1016/j.knosys.2015.09.018_bib0035
  article-title: Rough set
  publication-title: Int. J. Comput. Inf. Sci.
  doi: 10.1007/BF01001956
– volume: 2639
  start-page: 312
  year: 2003
  ident: 10.1016/j.knosys.2015.09.018_bib0040
  article-title: Variable precision Bayesian rough set model
  publication-title: Lect. Notes Comput. Sci.
  doi: 10.1007/3-540-39205-X_46
– volume: 29
  start-page: 81
  year: 1988
  ident: 10.1016/j.knosys.2015.09.018_bib0037
  article-title: Rough sets: probabilistic versus deterministic approach
  publication-title: Int. J. Man-Mach. Stud.
  doi: 10.1016/S0020-7373(88)80032-4
– volume: 6401
  start-page: 719
  year: 2010
  ident: 10.1016/j.knosys.2015.09.018_bib0056
  article-title: Naive Bayesian rough sets
  publication-title: Lect. Notes Comput. Sci.
  doi: 10.1007/978-3-642-16248-0_97
– volume: 20
  start-page: 119
  issue: Suppl. 1
  year: 2012
  ident: 10.1016/j.knosys.2015.09.018_bib0028
  article-title: Three-way government decision analysis with decision-theoretic rough sets
  publication-title: Int. J. Uncertain. Fuzziness Knowl.-Based Syst.
  doi: 10.1142/S0218488512400090
– start-page: 167
  year: 1994
  ident: 10.1016/j.knosys.2015.09.018_bib0018
  article-title: Variable precision rough sets with asymmetric bounds
– volume: 6954
  start-page: 504
  year: 2011
  ident: 10.1016/j.knosys.2015.09.018_bib0058
  article-title: Automatically determining the number of clusters using decision-theoretic rough set
  publication-title: Lect. Notes Comput. Sci.
  doi: 10.1007/978-3-642-24425-4_65
– volume: 49
  start-page: 255
  year: 2008
  ident: 10.1016/j.knosys.2015.09.018_bib0049
  article-title: Probabilistic rough set approximations
  publication-title: Int. J. Approx. Reason.
  doi: 10.1016/j.ijar.2007.05.019
– volume: 53
  start-page: 608
  year: 2012
  ident: 10.1016/j.knosys.2015.09.018_bib0032
  article-title: Probabilistic rough set over two universes and rough entropy
  publication-title: Int. J. Approx. Reason.
  doi: 10.1016/j.ijar.2011.12.010
– volume: 23
  start-page: 421
  year: 1968
  ident: 10.1016/j.knosys.2015.09.018_bib0060
  article-title: Probability measures of fuzzy events
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/0022-247X(68)90078-4
– volume: 41
  start-page: 225
  year: 2012
  ident: 10.1016/j.knosys.2015.09.018_bib0031
  article-title: On relationship between probabilistic rough set and Bayesian risk decision over two universes
  publication-title: Int. J. Gen. Syst.
  doi: 10.1080/03081079.2011.634067
– start-page: 491
  year: 2004
  ident: 10.1016/j.knosys.2015.09.018_bib0047
  article-title: Information granulation and approximation in a decision-theoretical model of rough sets
  publication-title: Cognit. Technol.
  doi: 10.1007/978-3-642-18859-6_19
– volume: 16
  start-page: 554
  year: 2014
  ident: 10.1016/j.knosys.2015.09.018_bib0016
  article-title: Generalized interval-valued fuzzy variable precision rough sets
  publication-title: Int. J. Fuzzy Syst.
– volume: 181
  start-page: 1080
  year: 2011
  ident: 10.1016/j.knosys.2015.09.018_bib0052
  article-title: The superiority of three-way decisions in probabilistic rough set models
  publication-title: Inf. Sci.
  doi: 10.1016/j.ins.2010.11.019
– volume: 5589
  start-page: 642
  year: 2009
  ident: 10.1016/j.knosys.2015.09.018_bib0050
  article-title: Three-way decision: an interpretation of rules in rough set theory
  publication-title: Lect. Notes Comput. Sci.
  doi: 10.1007/978-3-642-02962-2_81
– volume: 55
  start-page: 130
  year: 2014
  ident: 10.1016/j.knosys.2015.09.018_bib0021
  article-title: An axiomatic characterization of probabilistic rough sets
  publication-title: Int. J. Approx. Reason.
  doi: 10.1016/j.ijar.2013.02.012
– volume: 37
  start-page: 793
  year: 1992
  ident: 10.1016/j.knosys.2015.09.018_bib0046
  article-title: A decision theoretic framework for approximating concepts
  publication-title: Int. J. Man-Mach. Stud.
  doi: 10.1016/0020-7373(92)90069-W
– volume: 46
  start-page: 109
  year: 2013
  ident: 10.1016/j.knosys.2015.09.018_bib0003
  article-title: Recommender systems survey
  publication-title: Knowl.-Based Syst.
  doi: 10.1016/j.knosys.2013.03.012
– year: 1991
  ident: 10.1016/j.knosys.2015.09.018_bib0036
– year: 2013
  ident: 10.1016/j.knosys.2015.09.018_bib0009
– volume: 49
  start-page: 272
  year: 2008
  ident: 10.1016/j.knosys.2015.09.018_bib0068
  article-title: Probabilistic approach to rough sets
  publication-title: Int. J. Approx. Reason.
  doi: 10.1016/j.ijar.2007.06.014
– volume: 108
  start-page: 267
  year: 2011
  ident: 10.1016/j.knosys.2015.09.018_bib0010
  article-title: Game-theoretic rough sets
  publication-title: Fundam. Inf.
  doi: 10.3233/FI-2011-423
– year: 2015
  ident: 10.1016/j.knosys.2015.09.018_bib0029
  article-title: A novel three-way decision model based on incomplete information system
  publication-title: Knowl.-Based Syst.
– volume: 4585
  start-page: 360
  year: 2007
  ident: 10.1016/j.knosys.2015.09.018_bib0054
  article-title: Web-based support systems with rough set analysis
  publication-title: Lect. Notes Comput. Sci.
  doi: 10.1007/978-3-540-73451-2_38
– volume: 283
  start-page: 180
  year: 2014
  ident: 10.1016/j.knosys.2015.09.018_bib0042
  article-title: Decision-theoretic rough fuzzy set model and application
  publication-title: Inf. Sci.
  doi: 10.1016/j.ins.2014.06.045
– volume: 2
  start-page: 351
  year: 2006
  ident: 10.1016/j.knosys.2015.09.018_bib0014
  article-title: A novel approach in uncertain programming part I: new arithmetic and order relation for interval numbers
  publication-title: J. Ind. Manage. Optim.
  doi: 10.3934/jimo.2006.2.351
– start-page: 131
  year: 2002
  ident: 10.1016/j.knosys.2015.09.018_bib0039
  article-title: Bayesian rough set model
– start-page: 387
  year: 2015
  ident: 10.1016/j.knosys.2015.09.018_bib0053
  article-title: Probabilistic rough sets
– volume: 54
  start-page: 1410
  year: 2013
  ident: 10.1016/j.knosys.2015.09.018_bib0057
  article-title: Fuzzy probabilistic rough set model on two universes and its applications
  publication-title: Int. J. Approx. Reason.
  doi: 10.1016/j.ijar.2013.05.001
– volume: 4
  start-page: 66
  year: 2011
  ident: 10.1016/j.knosys.2015.09.018_bib0030
  article-title: Three-way investment decisions with decision-theoretic rough sets
  publication-title: Int. J. Comput. Intell. Syst.
  doi: 10.1080/18756891.2011.9727764
– volume: 281
  start-page: 21
  year: 2014
  ident: 10.1016/j.knosys.2015.09.018_bib0011
  article-title: Three-way decisions space and three-way decisions
  publication-title: Inf. Sci.
  doi: 10.1016/j.ins.2014.05.015
– year: 2015
  ident: 10.1016/j.knosys.2015.09.018_bib0022
  article-title: Sequential three-way decision and granulation for cost-sensitive face recognition
  publication-title: Knowl.-Based Syst.
– volume: 5009
  start-page: 676
  year: 2008
  ident: 10.1016/j.knosys.2015.09.018_bib0026
  article-title: Rough multi-category decision theoretic framework
  publication-title: Lect. Notes Comput. Sci.
  doi: 10.1007/978-3-540-79721-0_90
– volume: 298
  start-page: 534
  year: 2015
  ident: 10.1016/j.knosys.2015.09.018_bib0062
  article-title: Fuzzy and interval-valued fuzzy decision-theoretic rough set approaches based on the fuzzy probability measure
  publication-title: Inf. Sci.
  doi: 10.1016/j.ins.2014.12.008
– volume: 3641
  start-page: 294
  year: 2005
  ident: 10.1016/j.knosys.2015.09.018_bib0034
  article-title: Variable precision Bayesian rough set model and its application to human evaluation data
  publication-title: Lect. Notes Comput. Sci.
  doi: 10.1007/11548669_31
– year: 2015
  ident: 10.1016/j.knosys.2015.09.018_bib0038
  article-title: Decision-theoretic rough sets under dynamic granulation
  publication-title: Knowl.-Based Syst.
– volume: 4702
  start-page: 164
  year: 2007
  ident: 10.1016/j.knosys.2015.09.018_bib0006
  article-title: Statistical model for rough set approach to multicriteria classification
  publication-title: Lect. Notes Comput. Sci.
  doi: 10.1007/978-3-540-74976-9_18
– volume: 46
  start-page: 39
  year: 1993
  ident: 10.1016/j.knosys.2015.09.018_bib0064
  article-title: Variable precision rough set model
  publication-title: J. Comput. Syst. Sci.
  doi: 10.1016/0022-0000(93)90048-2
– volume: 21
  start-page: 1014
  year: 2009
  ident: 10.1016/j.knosys.2015.09.018_bib0027
  article-title: Rough cluster quality index based on decision theory
  publication-title: IEEE Trans. Knowl. Data Eng.
  doi: 10.1109/TKDE.2008.236
– start-page: 484
  year: 2010
  ident: 10.1016/j.knosys.2015.09.018_bib0020
  article-title: Hierarchical rough decision theoretic framework for text classification
– ident: 10.1016/j.knosys.2015.09.018_bib0012
– volume: 13
  start-page: 285
  year: 2000
  ident: 10.1016/j.knosys.2015.09.018_bib0023
  article-title: An information filtering model on the Web and its application in JobAgent
  publication-title: Knowl.-Based Syst.
  doi: 10.1016/S0950-7051(00)00088-5
– volume: 82
  start-page: 263
  year: 2003
  ident: 10.1016/j.knosys.2015.09.018_bib0066
  article-title: Attribute reduction in the Bayesian version of variable precision rough set model
  publication-title: Electron. Notes Theor. Comput. Sci.
  doi: 10.1016/S1571-0661(04)80724-2
– year: 1973
  ident: 10.1016/j.knosys.2015.09.018_bib0008
– volume: 6085
  start-page: 28
  year: 2010
  ident: 10.1016/j.knosys.2015.09.018_bib0063
  article-title: A three-way decision approach to email spam filtering
  publication-title: Lect. Notes Comput. Sci.
  doi: 10.1007/978-3-642-13059-5_6
– volume: 7413
  start-page: 287
  year: 2012
  ident: 10.1016/j.knosys.2015.09.018_bib0017
  article-title: Three-way decisions solution to filter spam email: an empirical study
  publication-title: Lect. Notes Comput. Sci.
  doi: 10.1007/978-3-642-32115-3_34
– volume: 276
  start-page: 186
  year: 2014
  ident: 10.1016/j.knosys.2015.09.018_bib0024
  article-title: Systematic studies on three-way decisions with interval-valued decision-theoretic rough sets
  publication-title: Inf. Sci.
  doi: 10.1016/j.ins.2014.02.054
– volume: 4481
  start-page: 1
  year: 2007
  ident: 10.1016/j.knosys.2015.09.018_bib0048
  article-title: Decision-theoretic rough set models
  publication-title: Lect. Notes Comput. Sci.
  doi: 10.1007/978-3-540-72458-2_1
– volume: 295
  start-page: 586
  year: 2015
  ident: 10.1016/j.knosys.2015.09.018_bib0001
  article-title: Interpretation of equilibria in game-theoretic rough sets
  publication-title: Inf. Sci.
  doi: 10.1016/j.ins.2014.10.046
– volume: 54
  start-page: 1087
  year: 2013
  ident: 10.1016/j.knosys.2015.09.018_bib0025
  article-title: Triangular fuzzy decision-theoretic rough sets
  publication-title: Int. J. Approx. Reason.
  doi: 10.1016/j.ijar.2013.03.014
– year: 1995
  ident: 10.1016/j.knosys.2015.09.018_bib0019
– volume: 21
  start-page: 869
  year: 2013
  ident: 10.1016/j.knosys.2015.09.018_bib0002
  article-title: Conditional density estimation using probabilistic fuzzy systems
  publication-title: IEEE Trans. Fuzzy Syst.
  doi: 10.1109/TFUZZ.2012.2235839
– volume: 40
  start-page: 81
  year: 2005
  ident: 10.1016/j.knosys.2015.09.018_bib0041
  article-title: The investigation of the Bayesian rough set model
  publication-title: Int. J. Approx. Reason.
  doi: 10.1016/j.ijar.2004.11.004
– volume: 20
  start-page: 191
  year: 1986
  ident: 10.1016/j.knosys.2015.09.018_bib0043
  article-title: Interval valued fuzzy sets based on normal forms
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/0165-0114(86)90077-1
– volume: 56
  start-page: 981
  year: 2012
  ident: 10.1016/j.knosys.2015.09.018_bib0005
  article-title: Credit scoring analysis using a fuzzy probabilistic rough set model
  publication-title: Comput. Stat. Data Anal.
  doi: 10.1016/j.csda.2011.06.036
– year: 1966
  ident: 10.1016/j.knosys.2015.09.018_bib0033
– volume: 44
  start-page: 849
  year: 2015
  ident: 10.1016/j.knosys.2015.09.018_bib0013
  article-title: Generalized interval-valued fuzzy variable precision rough sets determined by fuzzy logical operators
  publication-title: Int. J. Gen. Syst.
  doi: 10.1080/03081079.2015.1028540
– volume: 78
  start-page: 305
  year: 1996
  ident: 10.1016/j.knosys.2015.09.018_bib0004
  article-title: Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/0165-0114(96)84611-2
– volume: 87
  start-page: 442
  year: 2002
  ident: 10.1016/j.knosys.2015.09.018_bib0065
– volume: 21
  start-page: 357
  year: 1987
  ident: 10.1016/j.knosys.2015.09.018_bib0044
  article-title: Comparison of the probabilistic approximate classification and the fuzzy set model
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/0165-0114(87)90135-7
– volume: 8
  start-page: 338
  year: 1965
  ident: 10.1016/j.knosys.2015.09.018_bib0059
  article-title: Fuzzy sets
  publication-title: Inf. Control
  doi: 10.1016/S0019-9958(65)90241-X
– volume: 3641
  start-page: 283
  year: 2005
  ident: 10.1016/j.knosys.2015.09.018_bib0067
  article-title: Probabilistic rough sets
  publication-title: Lect. Notes Comput. Sci.
  doi: 10.1007/11548669_30
– start-page: 17
  year: 1990
  ident: 10.1016/j.knosys.2015.09.018_bib0045
  article-title: A decision-theoretic rough set model
– volume: 53
  start-page: 541
  year: 2012
  ident: 10.1016/j.knosys.2015.09.018_bib0061
  article-title: Bayesian rough set model: a further investigation
  publication-title: Int. J. Approx. Reason.
  doi: 10.1016/j.ijar.2011.12.006
SSID ssj0002218
Score 2.3744736
Snippet The concept of probabilistic rough sets, as a main subject of this paper, is intimately connected with the concept of decision-theoretic rough sets. This paper...
SourceID crossref
elsevier
SourceType Enrichment Source
Index Database
Publisher
StartPage 126
SubjectTerms Fuzzy event
Fuzzy probabilistic rough set
Interval-valued fuzzy event
Interval-valued fuzzy probabilistic rough set
Rough set
Three-way decisions
Title Fuzzy probabilistic rough sets and their corresponding three-way decisions
URI https://dx.doi.org/10.1016/j.knosys.2015.09.018
Volume 91
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3NS8MwFA9jXrz4Lc6PkYPXuKxNk_Y4hmMq7qKD3UKbJjCVbmwdsh38231JUz9AFLyUNiRQfn1575G-9_shdGlYEFBjNGFdZgjLjCIxBHa4wPbKTKxpZPud70d8OGa3k2jSQP26F8aWVXrfX_l05639SMej2ZlPp50HSA7AXiOb0tAwEpbxkzFhrfzq7bPMIwjcGZ-dTOzsun3O1Xg9F7Pl2pJ2dyPHdmqlP34KT19CzmAP7fhcEfeq19lHDV0coN1ahwH7bXmIbgerzWaNrTaM48u11MvYye_gpS6XOC1y7H4IYOW0OOYz18oCYwutyWu6xrlX2lkeofHg-rE_JF4jgShI9kuiDFU8TTjLQp0yJYRVlMp1GvMMvo2C4ANByjChLa-VESnAkdAszAKj4jSHu2PULGaFPkFYCWp4kmsRcs66Ac1iy8wCEczohCeGtVBYQyOVJxC3OhYvsq4Ue5IVoNICKmkiAdAWIh-r5hWBxh_zRY26_GYIEnz8rytP_73yDG3Dkz9ZOUfNcrHSF5BrlFnbGVMbbfVu7oajd7R11XQ
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3JasMwEB3S5NBeupemqw69iji2vB1DaMh-aQK5CVuWIG1xQhZK8vUdKXJoobTQizGyBsyzNDPIM-8BPCnmuo5SkrI6U5SlStAIAztecHulKpKOr_udB8OgPWbdiT8pQbPohdFlldb373y68dZ2pGbRrM2n09oLJge4Xn2d0jieH3oHUNHsVH4ZKo1Orz3cO2TXNcd8ej7VBkUHnSnzestny43m7a77hvBUq3_8FKG-RJ3WKRzbdJE0dm90BiWZn8NJIcVA7M68gG5rvd1uiJaHMZS5mn2ZGAUespSrJUnyjJh_AkQYOY75zHSz4NhCSvqRbEhmxXaWlzBuPY-abWplEqjAfH9FhXJEkMQBSz2ZMBGGWlQqk0kUpPh5BMYfjFOKhVJTW6kwQThiJ_VSV4koyfDuCsr5LJfXQEToqCDOZOgFAau7ThppchYMYkrGQaxYFbwCGi4sh7iWsnjnRbHYK98ByjWg3Ik5AloFurea7zg0_pgfFqjzb2uBo5v_1fLm35aPcNgeDfq83xn2buEIn9iDljsorxZreY-pxyp9sEvrEw8s2CU
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Fuzzy+probabilistic+rough+sets+and+their+corresponding+three-way+decisions&rft.jtitle=Knowledge-based+systems&rft.au=Zhao%2C+Xue+Rong&rft.au=Hu%2C+Bao+Qing&rft.date=2016-01-01&rft.pub=Elsevier+B.V&rft.issn=0950-7051&rft.eissn=1872-7409&rft.volume=91&rft.spage=126&rft.epage=142&rft_id=info:doi/10.1016%2Fj.knosys.2015.09.018&rft.externalDocID=S0950705115003573
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0950-7051&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0950-7051&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0950-7051&client=summon