fsets S3 class of linguistic fuzzy attributesThis function creates a set of linguistic fuzzy attributes from crisp data.
Numeric vectors, matrix or data frame columns are transformed into a set of
fuzzy attributes, i.e. columns with membership degrees. Factors and other
data types are transformed to fuzzy attributes by calling the fcut()
function.
lcut(x, ...)# S3 method for default
lcut(x, ...)
# S3 method for factor
lcut(x, name = deparse(substitute(x)), ...)
# S3 method for logical
lcut(x, name = deparse(substitute(x)), ...)
# S3 method for numeric
lcut(
x,
context = minmax,
atomic = c("sm", "me", "bi", "lm", "um", "ze", "neg.sm", "neg.me", "neg.bi",
"neg.lm", "neg.um"),
hedges = c("ex", "si", "ve", "ty", "-", "ml", "ro", "qr", "vr"),
name = deparse(substitute(x)),
hedgeParams = defaultHedgeParams,
...
)
# S3 method for data.frame
lcut(
x,
context = minmax,
atomic = c("sm", "me", "bi", "lm", "um", "ze", "neg.sm", "neg.me", "neg.bi",
"neg.lm", "neg.um"),
hedges = c("ex", "si", "ve", "ty", "-", "ml", "ro", "qr", "vr"),
...
)
# S3 method for matrix
lcut(x, ...)
An object of S3 class fsets is returned, which is a numeric matrix
with columns representing the fuzzy attributes. Each source column of the
x argument corresponds to multiple columns in the resulting matrix.
Columns will have names derived from used \(hedges\), atomic expression,
and \(name\) specified as the optional parameter.
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
following order of the hedges: \("ex" < "si" < "ve" < "-" < "ml" < "ro"
< "qr" < "vr"\) and \("ty" < "" < "ml" < "ro" < "qr" < "vr"\). Fuzzy
attributes created from the same source numeric vector (or column) would be
ordered that way, with other fuzzy attributes (from the other source) being
incomparable.
Data to be transformed: if it is a numeric vector, matrix, or data
frame, then the creation of linguistic fuzzy attributes takes place. For
other data types the fcut() function is called implicitly.
Other parameters to some methods.
A name to be added as a suffix to the created fuzzy attribute
names. This parameter can be used only if x is a numeric or logical
vector or a factor. If x is a matrix or data frame, name should be NULL
because the fuzzy attribute names are taken from column names of parameter
x. The name is also used as a value for the vars attribute of the
resulting fsets() instance.
A definition of context of a numeric attribute. It must be an
instance of an S3 class ctx3(), ctx5(), ctx3bilat() or ctx5bilat().
If x is a matrix or data frame then context should be a named list of
contexts for each x's column.
A vector of atomic linguistic expressions to be used for creation of fuzzy attributes.
A vector of linguistic hedges to be used for creation of fuzzy attributes.
Parameters that determine the shape of the hedges
Michal Burda
The aim of this function is to transform numeric data into a set of fuzzy
attributes. The resulting fuzzy attributes have direct linguistic
interpretation. This is a unique variant of fuzzification that is suitable
for the inference mechanism based on Perception-based Linguistic Description
(PbLD) -- see pbld().
A numeric vector is transformed into a set of fuzzy attributes accordingly to the following scheme:
\(<hedge> <atomic expression>\)
where \(<atomic expression>\) is an atomic linguistic expression, a value
from the following possibilities (note that the allowance of atomic
expressions is influenced with context being used - see ctx for details):
neg.bi: big negative (far from zero)
neg.um: upper medium negative (between medium negative and big negative)
neg.me: medium negative
neg.lm: lower medium negative (between medium negative and small
negative)
neg.sm: small negative (close to zero)
ze: zero
sm: small
lm: lower medium
me: medium
um: upper medium
bi: big
A \(<hedge>\) is a modifier that further concretizes the atomic expression (note that not each combination of hedge and atomic expression is allowed - see allowed.lingexpr for more details):
ex: extremely,
si: significantly,
ve: very,
ty: typically,
-: empty hedge (no hedging),
ml: more or less,
ro: roughly,
qr: quite roughly,
vr: very roughly.
Accordingly to the theory developed by Novak (2008), not every hedge is
suitable with each atomic #' expression (see the description of the hedges
argument). The hedges to be used can be selected with the hedges argument.
Function takes care of not to use hedge together with an unapplicable atomic
expression by itself.
Obviously, distinct data have different meaning of what is "small", "medium",
or "big" etc. Therefore, a context has to be set that specifies sensible
values for these linguistic expressions.
If a matrix (resp. data frame) is provided to this function instead of a single vector, all columns are processed the same way.
The function also sets up properly the vars() and specs() properties of
the result.
V. Novak, A comprehensive theory of trichotomous evaluative linguistic expressions, Fuzzy Sets and Systems 159 (22) (2008) 2939--2969.
fcut(), fsets(), vars(), specs()
# transform a single vector
x <- runif(10)
lcut(x, name='age')
# transform single vector with a custom context
lcut(x, context=ctx5(0, 0.2, 0.5, 0.7, 1), name='age')
# transform all columns of a data frame
# and do not use any hedges
data <- CO2[, c('conc', 'uptake')]
lcut(data)
# definition of custom contexts for different columns
# of a data frame while selecting only "ve" and "ro" hedges.
lcut(data,
context=list(conc=minmax,
uptake=ctx3(0, 25, 50)),
hedges=c('ve', 'ro'))
# lcut on non-numeric data is the same as fcut()
ff <- factor(substring("statistics", 1:10, 1:10), levels = letters)
lcut(ff)
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