The fuzzy QuickReduct algorithm based on FRST
Description
It is a function implementing the fuzzy QuickReduct algorithm
for feature selection based on FRST.
The fuzzy QuickReduct is a modification of QuickReduct based on RST (see FS.quickreduct.RST
).
Usage
1 2  FS.quickreduct.FRST(decision.table, type.method = "fuzzy.dependency",
type.QR = "fuzzy.QR", control = list())

Arguments
decision.table 
an object of a 
type.method 
a string representing the type of methods.
The complete description can be found in Section 
type.QR 
a string expressing the type of QuickReduct algorithm which is one of the two following algorithms:

control 
a list of other parameters as follows.
It should be noted that instead of supplying all the above parameters, we only set
those parameters needed by the considered method. See in Section 
Details
In this function, we provide an algorithm proposed by
(Jensen and Shen, 2002) which is fuzzy QuickReduct. Then, the algorithm has been modified by (Bhatt and Gopal, 2005) to improve stopping criteria.
This function is aimed to implement both algorithms. These algorithms can be executed by assigning the parameter type.QR
with "fuzzy.QR"
and "modified.QR"
for fuzzy quickreduct and modified fuzzy quickreduct
algorithms, respectively. Additionally, in the control
parameter, we provide one component which is
randomize
having boolean values: TRUE
or FALSE
. randomize = TRUE
means that
we evaluate some (or not all) attributes randomly along iteration. It will be useful if we have a large number of attributes
in a decision table.
In this function, we have considered many approaches of the lower and upper approximations.
The following list shows considered methods and their descriptions. Additionally, those approaches can be executed by
assigning the following value to the parameter type.method
.

"fuzzy.dependency"
: It is based on the degree of dependency using the implication/tnorm model approximation (Jensen and Shen, 2009). The detailed concepts about this approximation have been explained inB.IntroductionFuzzyRoughSets
andBC.LU.approximation.FRST
. 
"fuzzy.boundary.reg"
: It is based on the fuzzy boundary region proposed by (Jensen and Shen, 2009). This algorithm introduced the usage of the total uncertainty degree λ_B(Q) for all concepts of feature subset B and decision attribute Q. The total uncertainty degree is used as a parameter to select appropriate features. 
"vqrs"
: It is based on vaquely quantified rough set (VQRS) proposed by (Cornelis and Jensen, 2008). See alsoBC.LU.approximation.FRST
. 
"owa"
: Based on ordered weighted average (OWA) based fuzzy rough set, (Cornelis et al, 2010) proposed the degree of dependency as a parameter employed in the algorithm to select appropriate features. The explanation about lower and upper approximations based on OWA can be found inBC.LU.approximation.FRST
. 
"rfrs"
: It is based on degree of dependency that is obtained by performing the robust fuzzy rough sets proposed by (Hu et al, 2012). The detailed concepts about this approximation have been explained inBC.LU.approximation.FRST
. 
"min.positive.reg"
: Based on measure introduced in (Cornelis et al, 2010) which considers the most problematic element in the positive region, defined using the implicator/tnorm model. 
"fvprs"
: It is based on degree of dependency proposed by (Zhao et al, 2009). The degree is obtained by using fuzzy lower approximation based on fuzzy variable precision rough set model. 
"fuzzy.discernibility"
: This approach attempts to combine the the decisionrelative discernibility matrix and the fuzzy QuickReduct algorithm. (Jensen and Shen, 2009) introduced a measurement which is the degree of satisfaction to select the attributes. 
"beta.pfrs"
: Based on βprecision fuzzy rough sets (βPFRS) proposed by (Salido and Murakami, 2003), the degree of dependency as a parameter employed in the algorithm to select appropriate features. The explanation about lower and upper approximations based on βPFRS can be found inBC.LU.approximation.FRST
.
It should be noted that the parameter type.method
is related to parameter control
.
In other words, we only set the components in the control
parameter that related to the chosen type of method.
The following is a list showing the components of control
needed by each type of methods.

type.method = "fuzzy.dependency"
:control < list(t.implicator, type.relation, type.aggregation)

type.method = "fuzzy.boundary.reg"
:control < list(t.implicator, type.relation, type.aggregation)

type.method = "vqrs"
:control < list(alpha, q.some, q.most, type.aggregation)

type.method = "owa"
:control < list(t.implicator, type.relation, m.owa, type.aggregation)

type.method = "rfrs"
:control < list(t.implicator, type.relation, type.rfrs,
k.rfrs, type.aggregation)

type.method = "min.positive.reg"
:control < list(alpha, t.implicator, type.relation, type.aggregation)

type.method = "fuzzy.discernibility"
:control < list(alpha, t.implicator, type.relation, type.aggregation)

type.method = "fvprs"
:control < list(alpha.precision, t.implicator, type.relation, type.aggregation)

type.method = "beta.pfrs"
:control < list(t.implicator, type.relation, beta.quasi, type.aggregation)
The descriptions of each component can be seen in the documentation of the control
parameter.
It should be noted that this function does not give the new decision table directly.
An additional function called SF.applyDecTable
is used to produce new decision table based on
information about the reduct from this function. See Section Examples
.
Value
A class "FeatureSubset"
that contains the following components:

reduct
: a list representing a single reduct. In this case, it could be a superreduct or just a subset of feature. 
type.method
: a string representing the type of method. 
type.task
: a string showing the type of task which is"feature selection"
. 
model
: a string representing the type of model. In this case, it is"FRST"
which means fuzzy rough set theory.
Author(s)
Lala Septem Riza
References
C. Cornelis, G. Hurtado Martin, R. Jensen, and D. Slezak, "Feature Selection with Fuzzy Decision Reducts", Information Sciences, vol. 180, no. 2, p. 209  224 (2010).
C. Cornelis, N. Verbiest, and R. Jensen, "Ordered Weighted Average Based Fuzzy Rough Sets", Proceedings of the 5th International Conference on Rough Sets and Knowledge Technology (RSKT 2010), p. 78  85 (2010).
C. Cornelis and R. Jensen, "A Noisetolerant Approach to Fuzzyrough Feature Selection", Proceedings of the 2008 IEEE International Conference on Fuzzy Systems (FUZZIEEE 2008), p. 1598  1605 (2008).
J. M. F. Salido and S. Murakami, "Rough Set Analysis of a General Type of Fuzzy Data Using Transitive Aggregations of Fuzzy Similarity Relations", Fuzzy Sets Syst., vol. 139, p. 635  660 (2003).
Q. Hu, L. Zhang, S. An, D. Zhang, and D. Yu, "On Robust Fuzzy Rough Set Models", IEEE Trans. on Fuzzy Systems, vol. 20, no. 4, p. 636  651 (2012).
R. B. Bhatt and M. Gopal, "On Fuzzyrough Sets Approach to Feature Selection", Pattern Recognition Letters, vol. 26, no. 7, p. 965  975 (2005).
R. Jensen and Q. Shen, "Fuzzyrough Sets for Descriptive Dimensionality Reduction", In: Proceedings of IEEE International Conference on Fuzzy System, FUZZIEEE, p. 29  34 (2002).
R. Jensen and Q. Shen, "New Approaches to Fuzzyrough Feature Selection", IEEE Transactions on Fuzzy Systems, vol. 17, no. 4, p. 824  838 (2009).
S. Y. Zhao, E. C. C. Tsang, and D. G. Chen, "The Model of Fuzzy Variable Precision Rough Sets", IEEE Trans. Fuzzy Systems, vol. 17, no. 2, p. 451  467 (2009).
See Also
FS.quickreduct.RST
and FS.feature.subset.computation
.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84  ##########################################################
## Example 1: Dataset containing nominal values on all attributes
##########################################################
data(RoughSetData)
decision.table < RoughSetData$housing7.dt
########## using fuzzy lower approximation ##############
control < list(t.implicator = "lukasiewicz", type.relation = c("tolerance", "eq.1"),
type.aggregation = c("t.tnorm", "lukasiewicz"))
reduct.1 < FS.quickreduct.FRST(decision.table, type.method = "fuzzy.dependency",
type.QR = "fuzzy.QR", control = control)
########## using fuzzy boundary region ##############
## Not run: control < list(t.implicator = "lukasiewicz", type.relation = c("tolerance", "eq.1"),
type.aggregation = c("t.tnorm", "lukasiewicz"))
reduct.2 < FS.quickreduct.FRST(decision.table, type.method = "fuzzy.boundary.reg",
type.QR = "fuzzy.QR", control = control)
########## using vaguely quantified rough sets (VQRS) #########
control < list(alpha = 0.9, q.some = c(0.1, 0.6), q.most = c(0.2, 1),
type.aggregation = c("t.tnorm", "lukasiewicz"))
reduct.3 < FS.quickreduct.FRST(decision.table, type.method = "vqrs",
type.QR = "fuzzy.QR", control = control)
########## ordered weighted average (OWA) #########
control < list(t.implicator = "lukasiewicz", type.relation = c("tolerance", "eq.1"),
m.owa = 3, type.aggregation = c("t.tnorm","lukasiewicz"))
reduct.4 < FS.quickreduct.FRST(decision.table, type.method = "owa",
type.QR = "fuzzy.QR", control = control)
########## robust fuzzy rough sets (RFRS) #########
control < list(t.implicator = "lukasiewicz", type.relation = c("tolerance", "eq.1"),
type.rfrs = "k.trimmed.min", type.aggregation = c("t.tnorm", "lukasiewicz"),
k.rfrs = 0)
reduct.5 < FS.quickreduct.FRST(decision.table, type.method = "rfrs",
type.QR = "fuzzy.QR", control = control)
########## using min positive region (delta) ###########
control < list(alpha = 1, t.implicator = "lukasiewicz",
type.relation = c("tolerance", "eq.1"), type.aggregation =
c("t.tnorm", "lukasiewicz"))
reduct.6 < FS.quickreduct.FRST(decision.table, type.method = "min.positive.reg",
type.QR = "fuzzy.QR", control = control)
########## using FVPRS approximation ##############
control < list(alpha.precision = 0.05, t.implicator = "lukasiewicz",
type.aggregation = c("t.tnorm", "lukasiewicz"),
type.relation = c("tolerance", "eq.1"))
reduct.7 < FS.quickreduct.FRST(decision.table, type.method = "fvprs",
type.QR = "fuzzy.QR", control = control)
########## using beta.PFRS approximation ##############
control < list(t.implicator = "lukasiewicz", type.relation = c("tolerance", "eq.1"),
beta.quasi = 0.05, type.aggregation = c("t.tnorm", "lukasiewicz"))
reduct.8 < FS.quickreduct.FRST(decision.table, type.method = "beta.pfrs",
type.QR = "fuzzy.QR", control = control)
########## using fuzzy discernibility matrix ##############
control < list(alpha = 1, type.relation = c("tolerance", "eq.1"),
type.aggregation = c("t.tnorm", "lukasiewicz"),
t.implicator = "lukasiewicz")
reduct.9 < FS.quickreduct.FRST(decision.table, type.method = "fuzzy.discernibility",
type.QR = "fuzzy.QR", control = control)
## End(Not run)
##########################################################
## Example 2: Dataset containing nominal and continuous values
## In this case, we only provide one method but others work in
## the same way.
## In this example, we will show how to get the
## new decision table as well
##########################################################
data(RoughSetData)
decision.table < RoughSetData$hiring.dt
########## using fuzzy lower approximation ##############
control < list(type.aggregation = c("t.tnorm", "lukasiewicz"),
t.implicator = "lukasiewicz", type.relation = c("tolerance", "eq.1"))
reduct.1 < FS.quickreduct.FRST(decision.table, type.method = "fuzzy.dependency",
type.QR = "fuzzy.QR", control = control)
## get new decision table based on reduct
new.decTable < SF.applyDecTable(decision.table, reduct.1)
