R/card.capacity.R

In kappalab: Non-Additive Measure and Integral Manipulation Functions

##############################################################################
#
# Copyright © 2005 Michel Grabisch and Ivan Kojadinovic    
#
# Ivan.Kojadinovic@polytech.univ-nantes.fr
#
# This software is a package for the statistical system GNU R:
# http://www.r-project.org 
#
# This software is governed by the CeCILL license under French law and
# abiding by the rules of distribution of free software.  You can  use, 
# modify and/ or redistribute the software under the terms of the CeCILL
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## Class card.capacity extends card.game

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## Constructor from numeric
card.capacity <- function(object) {
    
    if (!is.numeric(object))
        stop("wrong argument")

    new("card.capacity", data = object, n = length(object) - 1)
}

## Constructor from card.set.func
setMethod("as.card.capacity", signature(object = "card.set.func"),
          function(object,...) {
              
              new("card.capacity", data = object@data, n = object@n)
          }
          )

## Constructor from capacity
setMethod("as.card.capacity", signature(object = "capacity"),
          function(object, ...) {
              
              csf <- as.card.set.func.internal(object)
              new("card.capacity", data = csf$data, n = csf$n)
          }
          )

## Constructor from card.capacity
## The conjugate of a capacity is a capacity
setMethod("conjugate", signature(object = "card.capacity"),
          function(object, ...) {
              
              card.capacity(object@data[object@n+1]
                            - object@data[(object@n+1):1])
          }
          )

## Constructors for simple capacities
lower.capacity <- function(n) {
    
    new("card.capacity", data = c(rep(0,n),1), n = n)
}

upper.capacity <- function(n) {
    
    new("card.capacity", data = c(0,rep(1,n)), n = n)
}

uniform.capacity <- function(n) {

    new("card.capacity", data = 0:n/n, n = n)
}

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## Tests whether the set function is normalized
setMethod("is.normalized", signature(object = "card.capacity"),
          function(object,...) {
              
              object@data[object@n+1] == 1
          }
          )

## Returns the normalized version of the capacity
setMethod("normalize", signature(object = "card.capacity"),
          function(object,...) {
              
              card.capacity(object@data / object@data[object@n+1])
          }
          )

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## Computes the orness of a capacity (normalized)
setMethod("orness", signature(object = "card.capacity"),
          function(object, ...) {
              return(sum(object@data[1:object@n])
                     / ((object@n - 1)
                        * object@data[object@n + 1]))
          }
          )

## Computes the veto indices, here equal to 1 - orness
setMethod("veto", signature(object = "card.capacity"),
          function(object, ...) {
              
              result <- 1 - orness(object)
              names(result) <- "All"
              result	
          }
          )

## Computes the favor indices, here equal to orness
setMethod("favor", signature(object = "card.capacity"),
          function(object, ...) {
              
              result <- orness(object)
              names(result) <- "All"
              result		
          }
          )

## Computes the normalized variance of a capacity
setMethod("variance", signature(object = "card.capacity"),
          function(object, ...) {
              
              (sum(((object@data[2:(object@n+1)] -
                     object@data[1:object@n])/object@data[object@n+1])^2) -
               1/object@n) * object@n / (object@n - 1)	
          }
          )

## Computes the normalized entropy of a capacity
setMethod("entropy", signature(object = "card.capacity"),
          function(object, ...) {	
          
              sum(sapply((object@data[2:(object@n+1)] - object@data[1:object@n])
                         / object@data[object@n+1],shannon.function)) /
                             log(object@n)		
          }
          )

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