lfl (version 1.0)

fcut: Transform data into a set of fuzzy attributes using triangular or raised cosine shapes of the fuzzy sets

Description

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).

Usage

fcut(x, ...)
## S3 method for class 'data.frame':
fcut(x, 
     breaks,
     name=NULL,
     type=c('triangle', 'raisedcos'),
     merge=1,
     parallel=FALSE,
     ...)
## S3 method for class 'numeric':
fcut(x, 
     breaks,
     name=deparse(substitute(x)),
     type=c('triangle', 'raisedcos'),
     merge=1,
     parallel=FALSE,
     ...)

Arguments

x

Data to be transformed: a vector, matrix, or data frame. Non-numeric data are allowed.

breaks

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 fuzz

name

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 n

type

The type of fuzzy sets to be considered. Currently, 'triangle' or 'raisedcos' may be provided. The type argument may be also a function of 4 arguments that from the value of the first argument, and co

merge

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

parallel

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

...

Other parameters to some methods.

Value

• 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.

Details

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.

See Also

lcut, farules, pbld vars, specs, cbind.fsets

Examples

# 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)))