Sugeno.integral-methods {kappalab} | R Documentation |
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
.
The Sugeno integral of
f
is computed from the Möbius transform of a game.
The Sugeno integral of f
is computed from a game.
The Sugeno integral of
f
is computed from a cardinal game.
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.
game-class
,
Mobius.game-class
,
card.game-class
.
## 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)