agop - Online Manual

tnorm_minimum {agop}R Documentation

t-norms

Description

Various t-norms. Each of these is a fuzzy logic generalization of the classical conjuntion operation.

Usage

tnorm_minimum(x, y)

tnorm_product(x, y)

tnorm_lukasiewicz(x, y)

tnorm_drastic(x, y)

tnorm_fodor(x, y)

Arguments

x

numeric vector with elements in [0,1]

y

numeric vector of the same length as x, with elements in [0,1]

Details

A function T: [0,1]\times [0,1]\to [0,1] is a t-norm if for all x,y,z\in [0,1] it holds: (a) T(x,y)=T(y,x); (b) if y≤ z, then T(x,y)≤ T(x,z); (c) T(x,T(y,z))=T(T(x,y),z); (d) T(x, 1)=x.

The minimum t-norm is given by T_M(x,y)=min(x, y).

The product t-norm is given by T_P(x,y)=xy.

The Lukasiewicz t-norm is given by T_L(x,y)=max(x+y-1,0).

The drastic t-norm is given by T_D(x,y)=0 iff x,y\in [0,1), and min(x, y) otherwise.

The Fodor t-norm is given by T_F(x,y)=0 iff x+y ≤ 1, and min(x, y) otherwise.

Value

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

References

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

See Also

Other fuzzy_logic: fimplication_fodor, fimplication_goedel, fimplication_goguen, fimplication_kleene, fimplication_lukasiewicz, fimplication_maximal, fimplication_minimal, fimplication_reichenbach, fimplication_rescher, fimplication_weber, fimplication_yager; fnegation_classic, fnegation_maximal, fnegation_minimal, fnegation_yager; tconorm_drastic, tconorm_fodor, tconorm_lukasiewicz, tconorm_minimum, tconorm_product


[Package agop version 0.2-0 Index]