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Build membership functions from knots

Source: R/eval_fuzzy.R
compute_mf.Rd

compute_mf_funs constructs a list of membership functions (one per evaluation level) from knot values. compute_mf evaluates a single indicator value against those functions, returning a membership vector.

Usage

compute_mf_funs(knots, .builder = "tri", ...)

compute_mf(x, knots, .builder = "tri", ...)

Arguments

knots

A numeric vector of length \(n \ge 2\) defining the characteristic values (peaks / centers) of each evaluation level.

.builder

A character string or function that specifies how membership functions are built from knots:

"tri"

(default) Piecewise linear (triangular + trapezoidal). First level decays linearly from 1 to 0 across [th[1], th[2]], last level rises from 0 to 1 across [th[n-1], th[n]], middle levels are isosceles triangles peaking at each knot.

"gauss"

Gaussian (normal) membership. First level is a right-half Gaussian decaying from 1 at th[1], last level is a left-half Gaussian rising to 1 at th[n], middle levels are full Gaussians centered at each knot. Pass sigma to control spread (default = mean(diff(knots)) / 3).

"sigmoid"

Sigmoid-based membership. First level uses a decreasing sigmoid, last level an increasing sigmoid, middle levels use difference-of-sigmoids (bell-shaped). Pass slope to control steepness (default = 5 / mean(diff(knots))).

User-supplied function

A function with signature function(knots, ...) that returns a list of \(n\) functions, each accepting a numeric vector x and returning membership values in \([0, 1]\).

...

Additional arguments passed to the builder (e.g. sigma for "gauss", slope for "sigmoid", or forwarded to a custom builder function).

x

Numeric vector, input values for which to compute membership.

Value

  • compute_mf_funs: A list of \(n\) functions, one per level.

  • compute_mf: A numeric vector of length \(n\) with membership degrees for each level.

Examples

# Triangular membership (default)
th = c(0.05, 0.15, 0.25, 0.5)
compute_mf(0.07, th)
#> [1] 0.8 0.2 0.0 0.0

# Gaussian membership with custom sigma
compute_mf(0.07, th, .builder = "gauss", sigma = 0.05)
#> [1] 9.231163e-01 2.780373e-01 1.533811e-03 8.705427e-17

# Sigmoid membership with custom slope
compute_mf(0.07, th, .builder = "sigmoid", slope = 20)
#> [1] 0.4013123399 0.1883274470 0.0366957707 0.0001840719

# Custom builder: exponential decay
exp_builder = function(knots, rate = 1) {
  n = length(knots)
  lapply(seq_len(n), function(i) {
    force(i)
    function(x) exp(-rate * abs(x - knots[i]))
  })
}
compute_mf(0.07, th, .builder = exp_builder, rate = 10)
#> [1] 0.81873075 0.44932896 0.16529889 0.01356856

if (FALSE) { # \dontrun{
# Visualise all levels for a given builder
mfs = compute_mf_funs(th, .builder = "gauss", sigma = 0.05)
plots = lapply(mfs, \(f) plot_mf(f, xlim = c(0, 0.6)))
gridExtra::grid.arrange(grobs = plots, nrow = 2)
} # }