# Transform data into a `fsets` S3 class of linguistic fuzzy attributes This 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. ```r lcut(x, ...) ## Default S3 method: lcut(x, ...) ## S3 method for class 'factor' lcut(x, name = deparse(substitute(x)), ...) ## S3 method for class 'logical' lcut(x, name = deparse(substitute(x)), ...) ## S3 method for class '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 class '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 class 'matrix' lcut(x, ...) ``` ## Arguments - `x`: 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. - `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 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. - `context`: 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. - `atomic`: A vector of atomic linguistic expressions to be used for creation of fuzzy attributes. - `hedges`: A vector of linguistic hedges to be used for creation of fuzzy attributes. - `hedgeParams`: Parameters that determine the shape of the hedges ## Returns 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: c("$\"ex\" < \"si\" < \"ve\" < \"-\" < \"ml\" < \"ro\"\n$", "$ < \"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. ## Details 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: $ $ where $$ is an atomic linguistic expression, a value from the following possibilities (note that the allowance of atomic expressions is influenced with `context` being used - see ctx for details): * `neg.bi`: big negative (far from zero) * `neg.um`: upper medium negative (between medium negative and big negative) * `neg.me`: medium negative * `neg.lm`: lower medium negative (between medium negative and small negative) * `neg.sm`: small negative (close to zero) * `ze`: zero * `sm`: small * `lm`: lower medium * `me`: medium * `um`: upper medium * `bi`: big A $$ 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. ## Examples ```r # 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) ``` ## References V. Novak, A comprehensive theory of trichotomous evaluative linguistic expressions, Fuzzy Sets and Systems 159 (22) (2008) 2939--2969. ## See Also `fcut()`, `fsets()`, `vars()`, `specs()` ## Author(s) Michal Burda

lcut function