kappalab (version 0.4-0)

Sipos.integral-methods: Sipos integral

Description

Computes the Sipos integral (also called symmetric Choquet integral) of a real-valued function with respect to a game. The game can be given either under the form of an object of class game, card.game or Mobius.game.

References

M. Grabisch and Ch. Labreuche (2002), The symmetric and asymmetric Choquet integrals on finite spaces for decision making, Statistical Papers 43, pages 37-52.

See Also

game-class, Mobius.game-class, card.game-class.

Examples

## a normalized capacity
mu <- capacity(c(0:13/13,1,1))

## and its M�bius transform
a <- Mobius(mu)

## a discrete function f
f <- c(0.1,-0.9,-0.3,0.8)

## the Sugeno integral of f w.r.t mu
Sipos.integral(mu,f)
Sipos.integral(a,f)

## a similar example with a cardinal capacity
mu <- uniform.capacity(4)
Sipos.integral(mu,f)