kappalab (version 0.4-0)

conjugate-methods: The conjugate (or dual) transform

Description

Computes the conjugate (also called the dual) of a set function. The conjugate of the conjugate of a game gives the original game back.

References

T. Murofushi and M. Sugeno (2000), Fuzzy measures and fuzzy integrals, in: M. Grabisch, T. Murofushi, and M. Sugeno Eds, Fuzzy Measures and Integrals: Theory and Applications, Physica-Verlag, pages 3-41.

See Also

capacity-class, card.capacity-class, set.func-class, card.set.func-class.

Examples

## a game
mu <- game(c(0,-7:7))
mu

## its conjugate 
conjugate(mu)
## and mu again 
conjugate(conjugate(mu))

## a similar example with the upper capacity
mu <- capacity(c(0,rep(1,15)))
mu
conjugate(mu)
conjugate(conjugate(mu))

## a similar example with an object of class card.capacity
mu <- upper.capacity(6)
mu
conjugate(mu)
conjugate(conjugate(mu))

## the conjugate of a set function is a game
mu <- set.func(-7:8)
mu
conjugate(mu)
mu <- card.set.func(-2:5)
conjugate(mu)