kappalab (version 0.4-12)

orness-methods: Orness degree

Description

Computes the orness degree of a Choquet integral from the underlying normalized capacity. The capacity can be given either under the form of an object of class capacity, card.capacity or Mobius.capacity.

Methods

object = "Mobius.capacity"

The orness degree is computed from the Möbius transform of a capacity.

object = "capacity"

The orness degree is computed directly from a capacity.

object = "card.capacity"

The orness degree is computed from a cardinal capacity.

References

J.-L. Marichal (2000), Behavioral analysis of aggregation in multicriteria decision aid, in Preferences and Decisions under Incomplete Knowledge, J. Fodor and B. De Baets and P. Perny Eds, Physica-Verlag, pages 153-178, 2000.

See Also

capacity-class,
Mobius.capacity-class,
card.capacity-class,
Mobius-methods.

Examples

## the upper capacity
mu <- capacity(c(0,rep(1,15)))

## the Choquet integral w.r.t mu behaves like the maximum operator
f <- c(0.1,0.1,0,0.9)
Choquet.integral(mu,f)

## its orness is 1
orness(mu)

## the same example with a Mobius.capacity object
a <- Mobius(mu)
Choquet.integral(a,f)
orness(a)

## the same example with a card.capacity object
mu <- upper.capacity(4)
Choquet.integral(mu,f)
orness(mu)