kappalab (version 0.4-12)

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.

Methods

object = "game", f = "numeric"

The Sipos or symmetric Choquet integral of f is computed from a game.

object = "Mobius.game", f = "numeric"

The Sipos or symmetric Choquet integral of f is computed from the Möbius transform of a game.

object = "card.game", f = "numeric"

The Sipos or symmetric Choquet integral of f is computed from a cardinal 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 Mobius 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)