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A Quick Overview of Operations and Applications in
Rough Set Theory
Dr. G. Lavanya Devi, M.Sujatha, and Dr. G.JayaSuma
Abstract---Rough set theory (RST) is a mathematical tool to deal
with the analysis of vagueness. It is used in machine learning
particularly in the areas of knowledge discovery, artificial
intelligence, inductive reasoning and decision support systems.
Feature selection (FS) is a process of identifying optimal attributes.
Many feature selection methods have been developed and are
reviewed critically in this paper, with particular emphasis on their
current limitations. The applications of rough set theory are
presented. The major challenges of rough set-based feature selection
are having a constraint that all the data should be discrete.
Keywords--- Classification, Feature Selection, Rough set.
I. INTRODUCTION
Many problems in machine learning involve high
dimensional descriptions of input features. It is therefore not
surprising that much research has been carried out on
dimensionality reduction [68, 38, 49, 21, 53].
Vagueness arises due to a lack of sharp distinctions or
boundaries in the data itself. This is typical of human
communication and reasoning. Rough sets can be said to
model ambiguity resulting from a lack of information through
set approximations.
II. ROUGH SELECTION
Rough set theory [1, 12, 23, 64, 35] is a conventional set
theory that supports approximations in decision making. It
possesses many features in common (to a certain extent) with
the Dempster-Shafer theory of evidence [2] and fuzzy set
theory [10, 50]. The rough set itself is the approximation of a
vague concept (set) by a pair of precise concepts, called lower
and upper approximations, which are a classification of the
domain of interest into disjoint categories. The lower
approximation is a description of the domain objects which
are known with certainty to belong to the subset of interest,
whereas the upper approximation is a description of the
objects which possibly belong to the subset.
Central to rough set theory is the concept of
indiscernibility. An information system ), having a
finite object set non-empty set (the universe of discourse)
and is a non-empty finite set of attributes such that
for every . is the set of values that
attribute.
Dr.G.Lavanya Devi, Assist Prof, College of Engineering Andhra
University, India.
M.Sujatha is a Ph.D student at Andhra University, India.
Dr. G.JayaSuma is H.OD of Information Technology at JNTU
Viziannagaram, India.
A. Indiscernibility
For any there is an associated equivalence relation ) ) { )| ) )} (1)
IF ) ) then are indiscernible by
attributes from P. The equivalence classes of the P-
indiscernibility relation are denoted[ ] .
B. Lower and Upper Approximations
Let is subset of , it is approximated using only
the data contained within P by constructing the P-lower and
P-upper approximations of X:
={ |[ ] } (2)
={ |[ ] } (3)
It is such a tuple ⟨ ⟩ that is called a rough set consider
the approximation of concept.
C. Positive, Negative and Boundary Regions
Let P and Q be equivalence relations over , then the
positive, negative and boundary regions are defined by:
) ⋃ ⁄ (4)
) ⋃ ⁄ (5)
) ⋃ ⁄ ⋃ ⁄ (6)
D. Feature Dependency and Significance
For , it can be said that Q depends on P in a degree
k (where [ ]) denoted P ⇒k Q, if:
) |
)|
| | (7)
) ⋃ ⁄ is the positive region of the
partition of the universe with respect to P (i.e. the set of all
elements that can be classified uniquely into sets of the
partition ⁄ in terms of P). If , Q is completely
dependent on P, Q is partially dependent (to a
degree - k) on P.
Accuracy of approximation coefficient can be defined by
rough set of vagueness in numerical terms
) | |
| | (8)
| | denotes the cardinality of and )
. If ) , is crisp with respect to I (the concept is
precise with respect to I), and otherwise, if ) , X is
rough with respect to I (the concept X is vague with respect to
I).
International Conference on Intelligent Systems, Control & Manufacturing Technology (ICICMT’2015) March 16-17, 2015 Abu Dhabi (UAE)
http://dx.doi.org/10.15242/IIE.E0315508 14
III. REDUCTION METHOD
A reduct is defined as a subset of minimal cardinality R of
the conditional attribute set C such that for a given set of
attributes D, ) ) .R is a minimal subset
{ } ) ) for all . This means that no
attributes without affecting the dependency degree.
The QUICKREDUCT algorithm (adapted from[3] attempts
to calculate a reduct without exhaustively generating all
possible subsets. The extensions of reducts can be
REVERSEREDUCT, which employs backward e elimination
of attributes. Variable precision rough sets (VPRS) [4]
extended rough set theory by the relaxation of the subset
operator. Their emphases is on recognizing data patterns
which represent statistical trends but not functional.
The objective of VPRS is to classify the objects based on
small error rate when compared with predefined level.
Reducts generated from an information system are
sensitive to changes in the system. This can be seen by
removing a randomly chosen set of objects from the original
object set. Those reducts frequently occurring in random
subtables can be considered to be stable; it is these reducts
that are encompassed by dynamic reducts [5]. Relative
Dependency Method is a feature selection method which is
based on an alternative dependency measure is presented. The
proposed technique facilitates computation of discernibility
functions or positive regions with reduced cost without
optimizations.
Tolerance-Based Method is another way of attempting to
handle imprecision is to introduce a measure of similarity of
attribute values and define the lower and upper approximation
based on these similarity measures.
TABLE I
FEATURE SELECTION FOR DECISION SYSTEM BASED ON THE ROUGH SET
THEORY APPROACH
Authors Purpose Description
Golan
and Ziarko
[6]
Feature
selection
Proposed rough set reduct methodology
which used Datalogic/R
Ruhe [40]
Feature selection
Applied the rough set approach for analysis of software engineering data
which resulted from goal-oriented
measurement Duntsch
and
Gediga
[69]
Feature
selection and
classification
Developed a software system „GROBIAN‟
which performed rough set data analysis
Starzik et al.
[91] [70]
Feature selection
Presented an expansion algorithm which allowed the generation of all reducts in a
much less time than the elimination
method Fujimori
et al.
[25]
Feature
selection and
classification
Applied rough set theory to the discharge
currents accompanied by tree
Vinterbo
and Ohrn [22]
Feature
selection and classification
Presented a problem of simplification
method that ensured a lower bound of the degree of approximation together with a
genetic algorithm minimal cost
approximate hitting sets discovery
Bakar et Feature Presented an algorithm based on rough set
al. [8]
[67]
selection approach and a dedicated decision related
binary integer programming (BIP) to find minimum size reducts
Vesa et al. [109]
[51]
Feature selection and
classification
Described preprocessing, rule generation and classification validation
Yin et al.
[65]
Feature
selection
Described a new approach for data
filtering which effectively reduced
granularity of attribute measurement and improved the statistical significance of
rules
Beynon
[62]
Feature
selection
Presented an investigation of the criteria
for a b-reduct within variable precision rough set (VPRS) model
Galvez et al.
[42]
Feature selection and
classification
Presented ConjuntosAproximados con Incertidumbre (CAI) model, a new
revision of the variable precision rough set
(VPRS) model with stronger rules which used less number of attributes in their
antecedents
Diaz and
Corchad
[9]
Feature
selection
Proposed a feature subset selection
algorithm based on a greedy strategy that
tried to maximize an information measure of entropy. It decreased the computation
effort for inducing a classifier
Hu] [61] Feature
selection and
classification
Presented a new approach which used
rough set theory and database operations
to construct a good ensemble of classifiers
Li and Liu
[28]
Feature selection
Proposed the feature reduction algorithm and the conditional entropy to
compute the relevance of attributes
Haiying
et al. [7]
Feature
selection and
classification
Presented the model and approach for
hierarchical fault diagnosis for substation
based on rough set theory
Questier et al.
[72]
Feature selection
Described the use of rough set theory to construct reducts in a supervised way for
reducing the number of features in an
unsupervised clustering
Zhang et
al. [39]
Feature
selection
Proposed a novel heuristic algorithm based
on rough set theory to find out the feature subset
Swiniarski and
Skowron
[24]
Feature selection
Presented an application of rough set method for feature selection in pattern
recognition
Wei [41]
Feature selection
Presented a new approach for the selection of attributes for the construction of
decision tree based on rough set theory.
The results showed that the rough set-based approach was a feasible way for the
selection of nodes of decision tree
Zhu and
Wang [52]
Feature
selection
Investigated some basic properties
covering generalized rough sets. Constructed a set of axioms to characterize
the covering lower approximation
operation
Muir et Feature Used binary decision diagram (BDD) for
International Conference on Intelligent Systems, Control & Manufacturing Technology (ICICMT’2015) March 16-17, 2015 Abu Dhabi (UAE)
http://dx.doi.org/10.15242/IIE.E0315508 15
al. [13] selection more efficient determination of the
discernibility function
Zhang
and Yao [63]
Feature
selection
Proposed two new rough set theory-based
feature selection techniques like average support heuristics (ASH) and
parameterized average support heuristic
(PASH)
Curry [8] Feature
selection and classification
Developed sampling theory using both the
original rough set model and its probabilistic extension variable precision
rough set (VPRS) model Kryszkie
wicz and
Cichon [66]
Feature
selection
Proposed a number of algorithms to
discover all generalized reducts
(preserving generalized decisions), all possible reducts (preserving upper
approximations) and certain reducts
(preserving lower approximations) Hu et al.
[26]
Feature
selection
Proposed a new rough sets model and
redefined the core attributes and reducts
based on relational algebra to take advantages of the very efficient set-
oriented database operations
Chen et al. [71]
Feature selection
Proposed a reasonable definition of parameterization reduction of soft sets and
compared it with the attribute reduction in
rough set theory
Thangav
el et al. [60]
Feature
selection and classification
Proposed Modified Quickreduct
Algorithm for feature selection compared with original Quickreduct and variable
precision rough set (VPRS). The proposed
algorithm generated minimal reducts as well as less number of rules
Thangav
el et al. [27]
Feature
selection and classification
Proposed an Accelerated Quickreduct
algorithm to select the features from the decision
IV. ROUGH SET THEORY EXTENSIONS
The conceptual simplicity of the rough set approach is
undoubtedly one of the main reasons for its success. The
tolerance rough set model (TRSM)] [29] can be useful for
application to real-valued data. TRSM employs a similarity
relation to minimize data as opposed to the indiscernibility
relation used in classical rough-sets. The variable precision
rough sets (VPRS) approach [37] extends rough set theory by
relaxing the subset operator. It was originally proposed in
order to analyze and identify data patterns which represent
statistical trends rather than those which are functional. The
Dominance-based Rough Set Approach (DRSA) [30] is an
extension of RST for multi-criteria decision analysis. In
contrast to traditional RST, DRSA employs a dominance
relation instead of an equivalence relation. This allows DRSA
to deal with the inconsistencies which are typical of criteria
and reference-ordered decision classes. In VQRS, it is
implicitly assumed that the approximations are fuzzy sets, i.e.
mapped from X to [0, 1], that evaluate the degree to which the
associated condition is fulfilled.
Fig. 1 Rough set theory extensions
V. APPLICATIONS
Rough set theory has been applied successfully almost in
all the areas. One of the major limitations of the traditional
rough set model in the real applications is the inefficiency in
the computation of core attributes and the generation of
reducts. In order to improve the efficiency of computing core
attributes and reducts, many novel approaches have been
developed. This section shows the various applications for
feature selection and classification. These applications are
summarized in Table II.
TABLE II
AN OVERVIEW OF APPLICATIONS
Authors Applications
Methods Results
An et al. [20]
Water
demand
KDD-R
Best error rate was 6.67%
and average error rate prediction was 10.27%
Komorowski and Ohrn [15]
Cardiac patients
ROSETTA
Described decreasing the
degrees of precision p, increases the accuracy. If
p = 1.0, accuracy = 88.3%
and if p = 0.5, accuracy = 95.9%
Nakayama et al.
[36]
Diabetic
database
Rough
analysis
Fitting rate 81.7% or
84.9% (fuzzy inference) was high for supporting
diagnosis of
Macroangiopathy Kusiak et al.]
[68]
Solitary
pulmonary
nodules (SPNs)
Primary and
confirmation
based on rough
analysis
Classification quality was
91.3% with diagnostic
accuracy 100%
Kusiak et al.
[58]
SPN and
engineering
datasets
Rough
analysis
Classification quality of
SPN was 91.3% with
diagnostic accuracy 100%. For Engineering dataset the
classification quality was
96.8% Breault [17] Pima
Indian
Diabetic Database
ROSETTA
The mean accuracy was
73.8% with 95% CI where
the previous researches produced 71.5% mean
accuracy with 63.3% CI
International Conference on Intelligent Systems, Control & Manufacturing Technology (ICICMT’2015) March 16-17, 2015 Abu Dhabi (UAE)
http://dx.doi.org/10.15242/IIE.E0315508 16
Swiniarski
[33]
Face
recognition
PCA, LVQ Produced the classification
accuracy of 97.3% for the
test set
Zhong and
Skowron[123]
[47]
Slope-
collapse
database
Rough sets
heuristics
(RSH) and rough sets
with boolean
reasoning (RSBR)
Among 24 attributes, 9
were selected
Hu and
Cercone[38]
[44]
Market
database
DB Deci, Average prediction
accuracy of DB Deci was
73.8% whereas C4.5 was 67.3%
Vesa et al. [14]
Test
network
Fuzzy C-
means clustering
(FCM), rough
sets
In an average 95% of data
are classified successfully. Rough sets generated 193
rules whereas FCM
produced 25 rules
Midelfart et al.
[31]
Gastric
tumors
Dynamic
reduct, IR classifier and
genetic
algorithm
This method was examined
with ROSETTA system. Most of the classifiers had
a very good accuracy and
high AUC value
Jensen and
Shen [48]
Water
Treatment Plant
database
Fuzzy-rough
feature selection
(FRFS)
Fuzzy rough method
selected fewer attributes and lower classification
error than crisp rough set
Shen and
Chouchoulas
[59]
Water
Treatment
Plant database
Quick reduct
II , RIA,
C4.5
RIA produced
classification accuracy of
97.3% while C4.5 produced 96.8%. RIA was
better than C4.5
Tay and Shen
[57]
Multi-
cylinder
diesel
engine
Rough
analysis
Distinguished the fault
types or inspect the
dynamic characteristic of
the machinery Shen and
Jensen [89]
[43]
Water
Treatment
Plant database
Fuzzy-rough
feature
selection (FRFS),
conventional
entropy, PCA,
random-based
FRFS produced better
accuracy (training accuracy
83.3% and testing accuracy 83.9%) than other methods
Li et al.
[19]
Text
categorizati
on
Case-based
reasoning
(CBR)
Proved that the
performance of document
reduction depends on the threshold „thr‟. In an
average if thr = 0.96,
43.6% of documents were reduced
Krishnaswamy
et al [46]
Data
mining and high
performanc
e computing
Rough
analysis technique
Measured the error rate of
San Diego Super Computing (SDSC) „95
and „96. SDSC 95 was
better than SDSC 96 on the average mean error
Warren et al. [56]
Solid waste managemen
t (SWM)
Modified RS1 Enabled to handle larger datasets as previous RS1
Zaluski et al.
[16]
Breast
cancer
LEM2, C4.5,
CN2,
Assistant86
Accuracy of original
dataset was 70.63% and
standard deviation was 8.4%. For reduced dataset,
the accuracy was 71.5%
and standard deviation was
6.06%
Hassanien
[45]
Breast
cancer
Rough
analysis
Rough set was a useful tool
for inductive learning and
valuable aid for building
expert systems
Hassanien and
Ali [54]
Mammogra
m dataset
Rough
analysis,
decision trees, neural
networks
Classification accuracy of
rough set was 93.1%,
decision Trees 83% and neural networks 90.34%
Li and Cercone
[32]
Geriatric
dataset
ROSETTA Generated rules with
support = 30% and
confidence = 80% Wilk et al.
[55]
Abdominal
pain
LEM2,
explore
Explore produced 83.99%
classification accuracy
whereas LEM2 produced 74.07%
Thangavel et al.
[18]
UCI
medical dataset
Improved
Quickreduct, Quickreduct,
C4.5
Improved Quick reduct
produced minimal reduct as well as minimal rule
from the dataset containing
large number of attributes
VI. CONCLUSION
Feature selection is a dynamic field closely connected to
data mining and other data processing techniques. This paper
attempts to survey this fast developing field, show some
effective applications, and point out interesting trends and
challenges. Research is required to overcome imitations
imposed when it is costly to visit large data sets multiple
times or access instances at random as in data streams. In
future work ,we use Big Data is becoming the new Final Frontier
for scientific data research and for business applications in rough set
analysis.
REFERENCES
[1] I. D¨untsch and G. Gediga. “Rough Set Data Analysis”. In: A. Kent & J.
G. Williams (Eds.) Encyclopedia of Computer Science and Technology,
Vol. 43, No. 28, pp. 281–301. 2000. [2] A. Skowron and J.W. Grzymala-Busse. “From rough set theory to
evidence theory”. In Advances in the Dempster-Shafer Theory of
Evidence, (R. Yager, M. Fedrizzi, and J. Kasprzyk eds.), John Wiley & Sons, Inc. 1994.
[3] A. Chouchoulas and Q. Shen. “Rough set-aided keyword reduction for
text categorization”. Applied Artificial Intelligence, Vol. 15, No. 9, pp. 843–873. 2001.
http://dx.doi.org/10.1080/088395101753210773
[4] W. Ziarko. “Variable Precision Rough Set Model”. Journal of Computer
and System Sciences, Vol. 46, No. 1, pp. 39–59. 1993.
http://dx.doi.org/10.1016/0022-0000(93)90048-2
[5] J. Bazan, A. Skowron, P. Synak. “Dynamic reducts as a tool for extracting laws from decision tables”. In Z. W. Ras, M. Zemankova
(Eds.), Proceedings of the 8th Symposium on Methodologies for
Intelligent Systems, Lecture Notes in Artificial Intelligence 869, Springer-Verlag, pp. 346–355. 1994.
[6] R.H. Golan, W. Ziarko, “A methodology for stock market analysis
utilizing rough set theory”, Proceedings of the IEEE/IAFE (1995) 32–40.
[7] D. Haiying, Z. Yubo, X. Junyi, “Hiearchical fault diagnosis for
substation based on rough set”,Proceedings of the Powercon4(2002) 2318-2321.
[8] B. Curry, “Sampling aspects of rough set theory”, Computational
Management Science 1 (2004) 151–178. http://dx.doi.org/10.1007/s10287-003-0007-0
International Conference on Intelligent Systems, Control & Manufacturing Technology (ICICMT’2015) March 16-17, 2015 Abu Dhabi (UAE)
http://dx.doi.org/10.15242/IIE.E0315508 17
[9] F. Diaz, J.M. Corchado, “The selection of relevant features and rough
sets”, in: Proceedings of 9th International Conference Espan˜ a, 2001
[10] Z. Pawlak and A. Skowron. “Rough membership functions”. In R.
Yager, M. Fedrizzi, J. Kacprzyk (eds.), Advances in the Dempster-
Shafer Theory of Evidence.
[11] C.-C. Chan, “A rough set approach to attribute generalization in data mining”,Information Sciences 107 (1998) 169–176.
http://dx.doi.org/10.1016/S0020-0255(97)10047-0
[12] Z. Pawlak. “Rough Sets”. International Journal of Computer and Information Sciences, Vol. 11, No. 5, pp. 341–356. 1982.
http://dx.doi.org/10.1007/BF01001956
[13] A. Muir, I. Duntsch, G. Gediga, “Rough set data representation using binary decision diagrams”, RACSAM, Rev. R. Acad. Cien. Serie A.
Mat 98 (1) (2004) 197–211.
[14] L. Vesa, L. Timo, L. Mikko, K. Hannu, “A comparison of fuzzy C-means clusteringand rough sets based classification in network data
analysis”,in: Proceedings of WSEAS NNA-FSFS-EC, Interlaken,
Switzerland, 2002. [15] J. Komorowski, A. Ohrn, “Modelling prognostic power of cardiac tests
using rough sets”, Artificial Intelligence in Medicine 15 (1999) 167–
191 http://dx.doi.org/10.1016/S0933-3657(98)00051-7
[16] J. Zaluski, R. Szoszkiewicz, J. Krysinski, J. Stefanowski, “Rough set
theory and decision rules in data analysis of breast cancer patients”, Transactions on Rough Sets 1, LNCS 3100 (2004) 375–391.[16]
[17] J.L. Breault, “Data mining diabetic databases: are rough sets a useful
addition”,Proceedings of the Computing Science and Statistics 33 (2001) 12001.
[18] K. Thangavel, P. Jaganathan, A. Pethalakshmi, M. Karnan, “Effective
classification with improved quick reduct for medical database using rough system”, Bioinformatics and Medical Engineering 05 (1) (2005)
7–14.
[19] Y. Li, S.C.-K. Shiu, S.K. Pal, J.N.-.K. Liu, “A rough-set based CBR approach for feature and document reduction in text categorization”, in:
Proceedings of the 3rd International Conference on Machine Learning
and Cybernetics, 2004 [20] A. An, C. Chan, N. Shan, N. Cercone, W. Ziarko, “Applying knowledge
discovery to predictwater- supply consumption “, Expert IEEE 12 (4)
(1997) 72–78. http://dx.doi.org/10.1109/64.608199
[21] H. Liu, H. Motoda (Eds). “Feature Extraction, Construction and Selection”: A Data Mining Perspective (Kluwer International Series in
Engineering & Computer Science), Kluwer Academic Publishers. 1998.
http://dx.doi.org/10.1007/978-1-4615-5725-8 [22] S. Vinterbo, A. Ohrn, “Minimal approximate hitting sets and rule
templates”, International Journal of Approximate Reasoning 25
(2000) 123–143 http://dx.doi.org/10.1016/S0888-613X(00)00051-7
[23] H. Sever. “The status of research on rough sets for knowledge discovery
in databases”. In Proceedings of the Second International Conference on Nonlin-ear Problems in Aviation and Aerospace (ICNPAA98), Vol. 2,
pp. 673–680. 1998.
[24] R.W. Swiniarski, A. Skowron, “Rough set methods in feature selection and recognition”, Pattern Recognition Letters 24 (2003) 833–849
http://dx.doi.org/10.1016/S0167-8655(02)00196-4
[25] S. Fujimori, K. Mikami, T. Kajiya, T. Inoue, “Study on discharge currents with rough set theory”, in: Proceedings of IEEE International
Symposium on Electrical Insulation, 1998, pp. 432–435
http://dx.doi.org/10.1109/ELINSL.1998.694826 [26] X. Hu, T.Y. Lin, J. Jianchao, “A new rough sets model based on
database systems”, Fundamenta Informaticae (2004) 1–18.
[27] K. Thangavel, A. Pethalakshmi, “Performance analysis of accelerated Quickreduct algorithm”, Proceedings of International Conference on
Computational Intelligence and Multimedia Applications; IEEE Xplore
2.0 2 (2007) 318–322. [28] K. Li, Y.-S. Liu, “Rough set based attribute reduction approach in data
mining”, in: Proceedings of the First International Conference on
Machine Learning and Cybernetics, 2002.
[29] J.W. Guan, D.A. Bell, “Rough computational methods for information”,
Artificial Intelligence 105 (1998) 77–103.
http://dx.doi.org/10.1016/S0004-3702(98)00090-3
[30] S. Greco, B. Matarazzo, and R. Slowi´nski. “Rough sets theory for multicriteria decision analysis”. European Journal of Operational
Research, vol. 129, no.1 pp.1–47, 2001.
http://dx.doi.org/10.1016/S0377-2217(00)00167-3
[31] H. Midelfart, J. Komorowski, K. Norsett, F. Yedetie, A.K. Sandwick,
A. Laegreid,”Learning rough set classifiers from gene expressions and
clinical data”, FundamentaInformaticae 53 (2002) 155–183.
[32] J. Li, N. Cercrone, “Empirical Analysis on the Geriatric Care Data Set
Using Rough Sets Theory”, Tech. Report, CS-2005-05, 2005.
[33] R.W. Swiniarski,” Rough sets methods in feature reduction and classification “,International Journal on Applied mathematics and
Computer Science 11 (3)(2001) 565–582
[34] Q. Hu, H. Zhao, Z. Xie, and, D. Yu. Consistency based attribute reduction.PAKDD 2007, LNAI 4426, Yang (Ed.), vol. 4426, pp. 96–
107, 2007.
[35] A. Skowron, S.K. Pal. “Special issue: Rough sets, pattern recognition and data mining”. Pattern Recognition Letters, Vol. 24, No. 6, pp. 829–
933. 2003.
[36] H. Nakayama, Y. Hattori, R. Ishii,” Rule extraction based on rough set theory andits application to medical data analysis”, Proceedings of
IEEESMC‟99 5 (1999) 924–929.
[37] W. Ziarko. “Variable Precision Rough Set Model”, JCSS, vol. 46, no. 1, pp.39–59, 1993.
http://dx.doi.org/10.1016/0022-0000(93)90048-2
[38] K. Kira and L.A. Rendell. “The feature selection problem: Traditional meth-ods and a new algorithm”. In Proceedings of Ninth National
Conference on Artificial Intelligence, pp. 129–134. 1992..
[39] J. Zhang, J. Wang, D. Li, H. He, J. Sun, “A New Heuristic Reduct Algorithm Base on Rough Sets Theory”, LNCS 2762, Springer-Verlag,
2003, pp. 247–253.
[40] G. Ruhe, “Rough set-based data analysis in goal-oriented software measurement”,Proceedings of METRICS (1996) 10–19.
http://dx.doi.org/10.1109/METRIC.1996.492439
[41] J.-M. Wei, “Rough set based approach to selection of node”, International Journal of Computational Cognition 1 (2) (2003) 25–40.
[42] J.F. Galvez, F. Diaz, P. Carrion, A. Garcia, “An application for
knowledge discovery based on a revision of VPRS model”, in: Rough Sets and Current Trends in Computing 2000, LNAI 2005, 2001, 296–
303.
[43] Q. Hu, Z. Xie, D. Yu. Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation, Pattern Recognition
vol. 40, pp. 3509–3521,2007.
http://dx.doi.org/10.1016/j.patcog.2007.03.017 [44] Shen, R. Jensen, “Selecting informative features with fuzzy-rough sets
and its application for complex systems monitoring”, Pattern Recognition 37 (2004) 1351–136 .
http://dx.doi.org/10.1016/j.patcog.2003.10.016
[45] A.-E. Hassanien, “Rough set approach for attribute reduction and rule generation”:a case of patients with suspected breast cancer, Journal of
the American Society for Information Science and Techno logy 55 (11)
(2004) 954–962. http://dx.doi.org/10.1002/asi.20042
[46] S. Krishnaswamy, S.W. Loke, A. Zaslavsky, “Estimating computation
times of dataintensive applications”, IEEE Distributed Systems Online 5 (4) (2004).
http://dx.doi.org/10.1109/MDSO.2004.1301253
[47] N. Zhong, A. Skowron,” A rough set-based knowledge discovery process”, International Journal of Applied Mathematics and Computer
Science 11 (3) (2001)603–619.
[48] R. Jensen, Q. Shen,”Fuzzy-rough sets for descriptive dimensionality reduction”, in:Proceedings of the 11th International Conference on
Fuzzy Systems, 2002, pp.29–34.
http://dx.doi.org/10.1109/FUZZ.2002.1004954 [49] P. Langley. “Selection of relevant features in machine learning”. In
Proceedings of the AAAI Fall Symposium on Relevance, pp. 1–5. 1994.
[50] M. Wygralak. “Rough sets and fuzzy sets - some remarks on interrelations”. Fuzzy Sets and Systems, vol. 29, No. 2, pp. 241–243.
1989.
http://dx.doi.org/10.1016/0165-0114(89)90197-8 [51] L. Vesa, L. Mikko, K. Hannu, “Network traffic classification using
rough sets”, in:Third WSEAS Symposium on Mathematical Methods
and Computational Techniques in Electrical Engineering, 2001. [52] W. Zhu, F.-Y. Wang, “Reduction and axiomization of covering
generalized rough sets”, Information Sciences 152 (2003) 217–230.
http://dx.doi.org/10.1016/S0020-0255(03)00056-2 [53] Q-H. Hu, and D-R. Yu. Variable precision dominance based rough set
model and reduction algorithm for preference-ordered data, Proceedings
of the 2004 International Conference on Machine Learning and Cybernetics, vol. 4, pp. 2279–2284, 2004.
International Conference on Intelligent Systems, Control & Manufacturing Technology (ICICMT’2015) March 16-17, 2015 Abu Dhabi (UAE)
http://dx.doi.org/10.15242/IIE.E0315508 18
[54] A.-E. Hassanien, J.M.H. Ali, “Enhanced rough sets rule reduction
algorithm for classification digital mammography”, intelligent system
journal, Freund &Pettman 13 2 ,2004.
[55] S.Z. Wilk, R. Slowinski, W. Michalowski, S. Greco, “Supporting triage
of children with abdominal pain in the emergency room”, European
Journal of Operational Research 160 (3) (2005) 696–709.
http://dx.doi.org/10.1016/j.ejor.2003.06.034
[56] R.H. Warren, J.A. Johnson, G.H. Huang, “Application of rough sets to environmental engineering models”, Transactions on Rough Sets 1,
LNCS 3100 (2004) 356–374.
[57] F.E.H. Tay, L. Shen, “Fault diagnosis based on rough set theory”, Engineering Applications of Artificial Intelligence 16 (2003) 39–43.
http://dx.doi.org/10.1016/S0952-1976(03)00022-8
[58] A. Kusiak, K.H. Kernstine, J.A. Kern, K.A. McLaughlin, T.L. Tseng, “Data mining:medical and engineering case studies”, Proceedings of the
Industrial EngineeringResearch (2000) 1–7.
[59] Q. Shen, A. Chouchoulas, “A rough-fuzzy approach for generating classification rules”, Pattern Recognition 35 (2002) 2425–2438.
http://dx.doi.org/10.1016/S0031-3203(01)00229-1
[60] K. Thangavel, A. Pethalakshmi, P. Jaganathan, “A comparative analysis of feature selection algorithms based on rough set theory”, International
Journal of Soft Computing 1 (4) (2006) 288–294.
[61] X. Hu, “Using rough sets theory and database operations to construct a good ensemble of classifiers for data mining applications”, Proceedings
of ICDM (2001) 233–240.
[62] M. Beynon, “Reducts within the variable precision rough sets model”: a further investigation, European Journal of Operational Research 134
(2001) 592–605.
http://dx.doi.org/10.1016/S0377-2217(00)00280-0 [63] M. Zhang, J.T. Yao, “A rough sets based approach to feature
selection”, fuzzy information, Processing NAFIPS‟04 vol 1,2004 434–
439 [64] A. Skowron, Z. Pawlak, J. Komorowski and L. Polkowski.”A rough set
perspective on data and knowledge. Handbook of data mining and
knowledge discovery”, pp. 134–149, Oxford University Press. 2002 [65] X. Yin, Z. Zhou, N. Li, S. Chen, “An Approach for Data Filtering
Based on Rough Set Theory”, LNCS 2118, Springer-Verlag, Berlin,
2001, pp. 367–374. http://dx.doi.org/10.1007/3-540-47714-4_33
[66] X. Yin, Z. Zhou, N. Li, S. Chen, “An Approach for Data Filtering Based on Rough Set Theory”, LNCS 2118, Springer-Verlag, Berlin,
2001, pp. 367–374.
http://dx.doi.org/10.1007/3-540-47714-4_33 [67] M. Kryszkiewicz, K. Cichon, “Towards scalable algorithms for
discovering rough set reducts”,Transactions on Rough Sets 1, LNCS
3100 (2004) 120–143.] [68] A.A. Bakar, Md.N. Sulaiman, M. Othman, M.H. Selamat , “Finding
minimal reduct with binary integer programming in data mining “:
Proceedings of the tencon, 2000,pp.141-149. [69] I. Duntsch, G. Gediga, “The rough set engine GROBIAN”, in:
Proceedings of the IMACS World Congress, vol. 4, 1997, pp. 613–
619. [70] J. Starzyk, D.E. Nelson, K. Sturtz, “Reduct generation in information
systems”, Bulletin of International Rough Set Society 3 ,1998, 19–22.
[71] D. Chen, E.C.C. Tsang, D.S. Yeung, X. Wang, “The parameterization reduction of soft sets and its applications”, International Journal on
Computers and Mathematics vol 49 ,2005 pp 757–763.
http://dx.doi.org/10.1016/j.camwa.2004.10.036
[72] F. Questier, I.A. Rollier, B. Walczak, D.L. Massart, “Application of
rough set theory to feature selection for unsupervised clustering”,
Chemometrics and Intelligent Laboratory Systems vol 63, 2002 pp.155–167.
http://dx.doi.org/10.1016/S0169-7439(02)00041-2
Dr.G.Lavanya Devi 1 , Assist Prof, College of
Engineering Andhra University . She is working
in CS&SE department. She has 13 years
experience in teaching. She pursued her Ph.D at
JNTU ,Hyderabab in 2010.Her area of interest
are Fuzzy Theory, Data Mining, Bioinformatics,
DataBases Systems, Network security,
Algorithm Analysis , automata theory, computer
communication and Networks, Image
Processing, Pattern Recognition.she is guiding 8 Ph.D scholars .She received
“YOUNG ENGINEER” award in the year 2011 in the field of Computer
Science by Institution of Engineers (INDIA). E-
mail:[email protected]. Phone number 9704637338
M.Sujatha2 received B.Tech degree from JNTU
University at Hyderabad in 2002. She received
M.Tech degree from JNTU University at Hyderabad in 2009. Her area of interest includes
Data Mining, Theory of Computation, Soft
Computing and Machine Learning. She pursuing her Ph.D at Andhra University. E-mail
:[email protected]. Phone number
9985842263
Dr.Jaya Suma3 G H.OD of Information
Technology at JNTU Viziannagaram. Her research
interest includes Data Mining, Network Security,
Artificial Intelligence, Computer Vision & Soft
Computing and Machine Learning. She pursued her
Ph.D at Andhra University Visakhapatnam. E-mail:[email protected]. Phone number
9849198738
.
International Conference on Intelligent Systems, Control & Manufacturing Technology (ICICMT’2015) March 16-17, 2015 Abu Dhabi (UAE)
http://dx.doi.org/10.15242/IIE.E0315508 19