sets (version 1.0-16)

fuzzyfuns: Fuzzy membership functions

Description

Fuzzy membership and set creator functions.

Usage

charfun_generator(FUN, height = 1)
fuzzy_tuple(FUN = fuzzy_normal, n = 5, ...,
                 universe = NULL, names = NULL)
is.charfun_generator(x)
fuzzy_normal(mean = NULL, sd = 1, log = FALSE, height = 1, chop = 0)
fuzzy_two_normals(mean = NULL, sd = c(1,1), log = c(FALSE, FALSE),
                  height = 1, chop = 0)
fuzzy_bell(center = NULL, cross = NULL, slope = 4, height = 1, chop = 0)
fuzzy_sigmoid(cross = NULL, slope = 0.5, height = 1, chop = 0)
fuzzy_trapezoid(corners = NULL, height = c(1,1),
                return_base_corners = TRUE)
fuzzy_triangular(corners = NULL, height = 1,
                 return_base_corners = TRUE)
fuzzy_cone(center = NULL, radius = 2, height = 1,
           return_base_corners = TRUE)
fuzzy_pi3(mid = NULL, min = NULL, max = NULL, height = 1,
          return_base_corners = TRUE)
fuzzy_pi4(knots, height = 1, return_base_corners = TRUE)
fuzzy_normal_gset(mean = NULL, sd = 1, log = FALSE, height = 1,
                  chop = 0, universe = NULL)
fuzzy_two_normals_gset(mean = NULL, sd = c(1,1), log = c(FALSE, FALSE),
                      height = 1, chop = 0, universe = NULL)
fuzzy_bell_gset(center = NULL, cross = NULL, slope = 4, height = 1,
                chop = 0, universe = NULL)
fuzzy_sigmoid_gset(cross = NULL, slope = 0.5, height = 1,
                   chop = 0, universe = NULL)
fuzzy_trapezoid_gset(corners = NULL, height = c(1,1), universe = NULL,
                     return_base_corners = TRUE)
fuzzy_triangular_gset(corners = NULL, height = 1, universe = NULL,
                      return_base_corners = TRUE)
fuzzy_cone_gset(center = NULL, radius = 2, height = 1, universe = NULL,
                return_base_corners = TRUE)
fuzzy_pi3_gset(mid = NULL, min = NULL, max = NULL, height = 1,
              universe = NULL, return_base_corners = TRUE)
fuzzy_pi4_gset(knots, height = 1,
               universe = NULL, return_base_corners = TRUE)

Arguments

x

An Robject.

n

Positive integer indicating the number of sets to be created, or integer vector of location parameters used to create the sets.

FUN

Function to be used for creating a membership function. Needs to be vectorized, i.e., is expected to take a vector of set elements and to return a vector of numeric values.

height

Numeric value in the unit interval specifying the height of the set resulting from applying the membership function to the universe, i.e., the maximum value to which the values will be scaled to.

chop

Threshold value below which the membership function is truncated, i.e., has a value of 0.

center, mean

Numeric mean value(s) used for the resulting membership function.

sd

Numeric scale factor(s) (standard deviation(s)) used for the resulting membership function.

radius

Double added/subtracted from center to get the base line corners of the cone.

log

Logical (vector), indicating whether normal or log-normal distributions should be used.

cross

Double indicating the cross-over point for the sigmoidal distribution.

slope

Double indicating the slope at the cross-over point.

corners

Double values (vector of length four) indicating the abscissas of the four corners of the resulting trapezoid.

min, mid, max

Doubles indicating the abscissas of the three spline knots $(\code{min}, 0)$, $(\code{mid}, \code{height})$ and $(\code{max}, 0)$ the curve passes through.

knots

Vector of doubles of length four indicating the abscissas of the spline knots the curve passes through.

return_base_corners

Logical indicating whether membership grades for the base line corner elements should be returned as small values (.Machine$double.eps) instead of 0. Otherwise, if a set is created from the memberships, the corner elements wou

universe

Universal set used for computing the memberships grades.

names

optional character vector of component labels for the return value.

...

Further arguments passed to FUN.

Value

• For charfun_generator, a generating function taking an argument list of parameters, and returning a membership function, mapping elements to membership values (from of the unit interval). For fuzzy_tuple, a tuple of n fuzzy sets. For is.charfun_generator, a logical.

  For fuzzy_foo_gset, a fuzzy set.

  For the other functions, a membership function.

Details

These functions can be used to create sets with certain membership patterns.

The core functions are function generators, taking parameters and returning a corresponding fuzzy function (i.e., with values in the unit interval). All of them are normalized, i.e., scaled to have a maximum value of height (default: 1):

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

charfun_generator takes a vectorized function as argument, returning a function normalized by height.

The fuzzy_foo_gset functions directly generate generalized sets from fuzzy_foo, using the values defined by universe, sets_options("universe"), or seq(0, 20, by = 0.1) (in that order, whichever is not NULL).

fuzzy_tuple generates a sequence of n sets based on any of the generating functions (except fuzzy_trapezoid and fuzzy_triangular). The chosen generating function FUN is called with n different values chosen along the universe passed to the first argument, thus varying the position or the resulting graph.

See Also

set, gset, and tuple for the set types, and plot.gset for the available plot functions.

Examples

## creating a fuzzy normal function
N <- fuzzy_normal(mean = 0, sd = 1)
N(-3:3)

## create a fuzzy set with it
gset(charfun = N, universe = -3:3)

## same using wrapper
fuzzy_normal_gset(universe = -3:3)

## creating a user-defined fuzzy function
fuzzy_poisson <- charfun_generator(dpois)
gset(charfun = fuzzy_poisson(10), universe = seq(0, 20, 2))

## creating a series of fuzzy normal sets
fuzzy_tuple(fuzzy_normal, 5)

## creating a series of fuzzy cones with specific locations
fuzzy_tuple(fuzzy_cone, c(2,3,7))