The aim of the
fsets S3 class is to store several fuzzy sets in the
form of numeric matrix where columns represent fuzzy sets, rows are
elements from the universe, and therefore a value of
i-th row and
column is a membership degree of
i-th element of the universe to
fsets object also stores the information about
the origin of the fuzzy sets as well as a relation of specificity among
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A matrix of membership degrees. Columns of the matrix represent fuzzy sets, colnames are names of the fuzzy sets (and must not be NULL). Rows of the matrix represent elements of the universe.
A character vector that must correspond to the
A square numeric matrix containing values from
An instance of S3 class
Attribute values to be set to the object.
fsets() function is a constructor of an object of type
Each object stores two attributes:
specs. The functions
specs()). can be used to access these attributes.
It is assumed that the fuzzy sets
are derived from some raw variables, e.g. numeric vectors or factors.
attribute is a character vector of names of raw variables with size equal
to the number of fuzzy sets in
fsets object. It is then assumed that
two fuzzy sets with the same name in
vars() attribute are derived from
the same variable.
specs attribute gives a square numeric matrix of size equal to the number
of fuzzy sets in
specs[i][j] == 1 if and only if the
set is more specific than
j-th fuzzy set. Specificity of fuzzy sets means
the nestedness of fuzzy set: for instance,
very small is more specific than
extremely big is more specific than
very big; on the
very big and
extremely small are incomparable. A necessary
condition for specificity is subsethood.
fsets() returns an object of S3 class
a vector of original variable names of the
returns the specificity matrix.
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# create a matrix of random membership degrees m <- matrix(runif(30), ncol=5) colnames(m) <- c('a1', 'a2', 'a12', 'b1', 'b2') # create vars - first three (a1, a2, a3) and next two (b1, b2) # fuzzy sets originate from the same variable v <- c('a', 'a', 'a', 'b', 'b') names(v) <- colnames(m) # create specificity matrix - a1 and a2 are more specific than a12, # the rest is incomparable s <- matrix(c(0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), byrow=TRUE, ncol=5) colnames(s) <- colnames(m) rownames(s) <- colnames(m) # create a valid instance of the fsets class o <- fsets(m, v, s)
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