fnegation_yager {agop}

Fuzzy Negations

Description

Various fuzzy negations. Each of these is a fuzzy logic generalization of the classical negation operation.

Usage

fnegation_yager(x)

fnegation_classic(x)

fnegation_minimal(x)

fnegation_maximal(x)

Arguments

x

numeric vector with elements in [0,1]

Details

A function N: [0,1]\to [0,1] is a fuzzy implication if for all x,y\in [0,1] it holds: (a) if x\le y, then N(x)\ge N(y); (b) N(1)=0; (c) N(0)=1.

The classic fuzzy negation is given by N_C(x)=1-x.

The Yager fuzzy negation is given by N_Y(x)=sqrt(1-x^2).

The minimal fuzzy negation is given by N_0(x,y)=1 iff x=0, and 0 otherwise.

The maximal fuzzy negation is given by N_1(x,y)=1 iff x<1, and 0 otherwise.

Value

Numeric vector of the same length as x. The ith element of the resulting vector gives the result of calculating N(x[i]).

References

Klir G.J, Yuan B., Fuzzy sets and fuzzy logic. Theory and applications, Prentice Hall PTR, New Jersey, 1995.

Gagolewski M., Data Fusion: Theory, Methods, and Applications, Institute of Computer Science, Polish Academy of Sciences, 2015, 290 pp. isbn:978-83-63159-20-7

See Also

Other fuzzy_logic: fimplication_minimal(), tconorm_minimum(), tnorm_minimum()