kappalab (version 0.4-12)

Sugeno.integral-methods: Sugeno integral

Description

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 Möbius 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)