Defuzz (IVFN or TFN)

Convert a fuzzy number to a crisp value. For IVFNs, return the average of the upper and lower bounds. For TFNs, return the average of the lower bound, the mode, and the upper bound.

Usage

defuzz_ivfn_or_tfn(fuzzy_number)

Arguments

fuzzy_number

[ivfn or tfn] An IVFN or TFN object

Value

[numeric(1)]
A crisp number representative of the input fuzzy number.

Details

Defuzz-ing an IVFN to a crisp number: $$ \left[ x^{L} ,\ x^{U}\right] \ \mapsto \ \frac{x^{L} +x^{U}}{2} $$ where \(x^{L}, and x^{U}\) are the lower and upper bounds of the IVFN.

Defuzz-ing a TFN to a crisp number: $$ \left[ x^{L} ,\ x^{M} ,\ x^{U}\right] \ \mapsto \ \frac{x^{L} +x^{M} +x^{U}}{3} $$

where \(x^{L}, x^{M}, and x^{U}\) are the lower bound, mode, and upper bound of the TFN.

Examples

defuzz_ivfn_or_tfn(ivfn(-1, 1))
#> [1] 0
defuzz_ivfn_or_tfn(tfn(-1, 0, 1))
#> [1] 0