defuzz {lfl}

Convert fuzzy set into a crisp numeric value

Description

Take a fuzzy set in the form of a vector of membership degrees and a vector of numeric values that correspond to that degrees and perform a selected type of defuzzification, i.e. conversion of the fuzzy set into a single crisp value.

Usage

defuzz(degrees, values, type = c("mom", "fom", "lom", "dee"))

Arguments

degrees

A fuzzy set in the form of a numeric vector of membership degrees of values provided as the values argument.

values

A universe for the fuzzy set.

type

Type of the requested defuzzification method. The possibilities are:

• 'mom': Mean of Maxima - maximum membership degrees are found and a mean of values that correspond to that degrees is returned;

• 'fom': First of Maxima - first value with maximum membership degree is returned;

• 'lom': Last of Maxima - last value with maximum membership degree is returned;

• 'dee': Defuzzification of Evaluative Expressions - method used by the pbld() inference mechanism that combines the former three approaches accordingly to the shape of the degrees vector: If degrees is non-increasing then 'lom' type is used, if it is non-decreasing then 'fom' is applied, else 'mom' is selected.

Details

Function converts input fuzzy set into a crisp value. The definition of input fuzzy set is provided by the arguments degrees and values. These arguments should be numeric vectors of the same length, the former containing membership degrees in the interval [0, 1] and the latter containing the corresponding crisp values: i.e., values[i] has a membership degree degrees[i].

Value

A defuzzified value.

Author(s)

Michal Burda

See Also

fire(), aggregateConsequents(), perceive(), pbld(), fcut(), lcut()

Examples

# returns mean of maxima, i.e., mean of 6, 7, 8
defuzz(c(0, 0, 0, 0.1, 0.3, 0.9, 0.9, 0.9, 0.2, 0),
       1:10,
       type='mom')