sigmoidal: sigmoidal membership functions

In CFL: Compensatory Fuzzy Logic

Description

By theoretical considerations in (Dubois and Prade, 1985), it is recommend the use of sigmoidal membership functions for increasing or decreasing functions. The parameters of these functions are determined by setting three values. The first value is the variable that need fuzzification, The second is the value at which it is considered that the statement in the predicate is true (gamma). The third is the value for which the data makes almost unacceptable the corresponding statement (beta).

Usage

sigmoidal(x,ganma, beta)

Arguments

x	numeric, complex or vectors with values to fuzzificated.
ganma	Acceptable Value. Value in the range 0 and 1.
beta	Value almost unacceptable. Value in the range 0 and 1.

Details

The sigmoidal membership functions is used to fuzzificated values. The formula is:

S(x,α,γ)=1/(1+e^(-α(x-γ)))

where:

α=(ln(0.9)-ln(0.1))(γ-β)

Value

The sigmoidal membership functions return a value in the range [0...1].

Author(s)

Pablo Michel Marin Ortega, Kornelius Rohmeyer

References

Ceruto Cordov\'es, T.R.S., Alejandro \& Esp\'in Andrade, Rafael (2009) Descubrimiento de predicados a trav\'es de la b\'usqueda metaheur\'istica.

Examples

sigmoidal(20,0.5,0.1) 

CFL documentation built on May 2, 2019, 5:18 p.m.