This function creates a set of fuzzy attributes from crisp data. Factors, numeric vectors,
matrix or data frame columns are transformed into a set of fuzzy attributes, i.e. columns with
membership degrees. Unlike lcut, for transformation is not used the linguistic
linguistic approach, but partitioning using regular shapes of the fuzzy sets (such as triangle,
raised cosine).
fcut(x, ...)
# S3 method for data.frame
fcut(x,
breaks,
name=NULL,
type=c('triangle', 'raisedcos'),
merge=1,
parallel=FALSE,
...)
# S3 method for numeric
fcut(x,
breaks,
name=deparse(substitute(x)),
type=c('triangle', 'raisedcos'),
merge=1,
parallel=FALSE,
...)Data to be transformed: a vector, matrix, or data frame. Non-numeric data are allowed.
This argument determines the break-points of the positions of the fuzzy sets. It should be an ordered vector of numbers such that the \(i\)-th index specifies the beginning, \((i+1)\)-th the center, and \((i+2)\)-th the ending of the \(i\)-th fuzzy set.
I.e. the minimum number of breaks-points is 3; \(n-2\) elementary fuzzy sets would be created for \(n\) break-points.
If considering an i-th fuzzy set
(of type='triangle'), x values lower than \(i\)-th break (and greater than
\((i+2)\)-th break) would result in zero memberhsip degree, values equal to \((i+1)\)-th
break would have membership degree equal 1 and values between them the appropriate membership
degree between 0 and 1.
The resulting fuzzy sets would be named after the original data by adding dot (".") and a number \(i\) of fuzzy set.
Unlike cut, x values, that are lower or greater than the given
break-points, will have all memberhsip degrees equal to zero.
For non-numeric data, this argument is ignored. For x being a numeric vector, it must
be a vector of numeric values. For x being a numeric matrix or data frame, it must
be a named list containing a numeric vector for each column - if not, the values are
repeated for each column.
A name to be added as a suffix to the created fuzzy attribute names. This parameter
can be used only if x is a vector. If x is a matrix or data frame,
name should be NULL because the fuzzy attribute names are taken from column names
of the argument x.
The type of fuzzy sets to create Currently, 'triangle' or 'raisedcos'
may be used. The type argument may be also a function of 4 arguments that from
the value of the first argument, and considering the boundaries given by the next 3
arguments, computes a membership degree. See e.g. triangle or
raisedcos for details on how such function should look like.
This argument determines whether to derive additional fuzzy sets by merging the elementary
fuzzy sets (whose position is determined with the breaks argument) into super-sets.
The argument is ignored for non-numeric data in x.
merge may contain any integer number from 1 to length(breaks) - 2.
Value 1 means that the elementary fuzzy sets should be present in the output.
Value 2 means that the two consecutive elementary fuzzy sets should be combined by
using the Lukasiewic t-conorm, value 3 causes combining three consecutive elementary
fuzzy sets etc.
The names of the derived (merged) fuzzy sets is derived from the names of the original elementary fuzzy sets by concatenating them with the "|" (pipe) separator.
Whether the processing should be run in parallel or not. Parallelization is
implemented using the foreach package. The parallel environment must be
set properly in advance, e.g. with the registerDoMC() function of the doMC package.
Currently this argument is applied only if x is a matrix or data frame.
Other parameters to some methods.
An object of class "fsets" is returned, which is a numeric matrix with columns representing the
fuzzy attributes. Each source columm
of the x argument corresponds to multiple columns in the resulting matrix.
Columns have names that indicate the name of the source as well as a index \(i\) of fuzzy set(s)
-- see the description of arguments breaks and merge above.
The resulting object would also have set the vars and specs
properties with the former being created from original column names (if x is a matrix or
data frame) or the name argument (if x is a numeric vector). The
specs incidency matrix would be created to reflect the superset-hood of the merged
fuzzy sets.
The aim of this function is to transform numeric data into a set of fuzzy attributes. The result is in the form of the object of class "fsets", i.e. a numeric matrix whose columns represent fuzzy sets (fuzzy attributes) with values being the membership degrees.
The function behaves diffently to the type of input x.
If x is a factor or a logical vector (or other non-numeric data) then for each distinct
value of an input, a fuzzy set is created, and data would be transformed into crisp membership
degrees 0 or 1 only.
If x is a numeric vector then fuzzy sets are created accordingly to break-points
specified in the breaks argument with 1st, 2nd and 3rd break-point specifying the first
fuzzy set, 2nd, 3rd and 4th break-point specifying th second fuzzy set etc. The shape of the
fuzzy set is determined by the type argument that may be equal either to a string
'triangle' or 'raisedcos' or it could be a function that computes the membership
degrees for itself (see triangle or raisedcos functions for
details). Additionally, super-sets of these elementary sets may be created by specifying the
merge argument. Values of this argument specify how many consecutive fuzzy sets should be
combined (by using the Lukasiewic's t-conorm) to produce super-sets - see the description of
merge above.
If a matrix (resp. data frame) is provided to this function instead of single vector, all columns are
processed separately as described above and the result is combined with the
cbind.fsets function.
The function sets up properly the vars and specs properties of
the result.
# NOT RUN {
# fcut on non-numeric data
ff <- factor(substring("statistics", 1:10, 1:10), levels = letters)
fcut(ff)
# transform a single vector into a single fuzzy set
x <- runif(10)
fcut(x, breaks=c(0, 0.5, 1), name='age')
# transform single vector into a partition of the interval 0-1
# (the boundary triangles are right-angled)
fcut(x, breaks=c(0, 0, 0.5, 1, 1), name='age')
# also create supersets
fcut(x, breaks=c(0, 0, 0.5, 1, 1), name='age', merge=c(1, 2))
# transform all columns of a data frame
# with different breakpoints
data <- CO2[, c('conc', 'uptake')]
fcut(data, breaks=list(conc=c(95, 95, 350, 1000, 1000),
uptake=c(7, 7, 28.3, 46, 46)))
# }
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