Computes the Sugeno integral of a non negative function with
respect to a game. Moreover, if the game is a capacity, the range of the function must be contained into
the range of the capacity. The game can be given either under the form of an
object of class game, card.game or Mobius.game.
Methods
object = "Mobius.game", f = "numeric"
The Sugeno integral of
f is computed from the M<c3><b6>bius transform of a game.
object = "game", f = "numeric"
The Sugeno integral of f
is computed from a game.
object = "card.game", f = "numeric"
The Sugeno integral of
f is computed from a cardinal game.
References
M. Sugeno (1974), Theory of fuzzy integrals and its applications, Tokyo
Institute of Technology, Tokyo, Japan.
J-L. Marichal (2000), On Sugeno integral as an aggregation function, Fuzzy Sets
and Systems 114, pages 347-365.
J-L. Marichal (2001), An axiomatic approach of the discrete Sugeno integral as a
tool to aggregate interacting criteria in a qualitative framework, IEEE
Transactions on Fuzzy Systems 9:1, pages 164-172.
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
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
Sugeno.integral(mu,f)
Sugeno.integral(a,f)
## a similar example with a cardinal capacity
mu <- uniform.capacity(4)
Sugeno.integral(mu,f)