https://github.com/cran/kappalab
Tip revision: c35c3217a80758cae846a0c1336934ca8aee9b2b authored by Ivan Kojadinovic on 23 September 2006, 00:00:00 UTC
version 0.3-0
version 0.3-0
Tip revision: c35c321
lin.prog.capa.ident.R
##############################################################################
#
# Copyright ゥ 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
# license as circulated by CEA, CNRS and INRIA at the following URL
# "http://www.cecill.info".
#
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# modify and redistribute granted by the license, users are provided only
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##############################################################################
## Capacity identification using the linear programming based approach
## of Marichal and Roubens
##############################################################################
## Constructs a Mobius.capacity object by means of a linear program
lin.prog.capa.ident <- function(n, k,
A.Choquet.preorder = NULL,
A.Shapley.preorder = NULL,
A.Shapley.interval = NULL,
A.interaction.preorder = NULL,
A.interaction.interval = NULL,
A.inter.additive.partition = NULL,
epsilon = 1e-6) {
## check n and k
if (!(as.integer(n) == n && k %in% 1:n))
stop("wrong arguments")
## check A.Choquet.preorder
if (!((is.matrix(A.Choquet.preorder)
&& dim(A.Choquet.preorder)[2] == 2*n+1)
|| is.null(A.Choquet.preorder)))
stop("wrong Choquet preorder constraint matrix")
## check A.Shapley.preorder
if (!((is.matrix(A.Shapley.preorder) && dim(A.Shapley.preorder)[2] == 3)
|| is.null(A.Shapley.preorder)))
stop("wrong Shapley preorder constraint matrix")
## check A.Shapley.interval
if (!((is.matrix(A.Shapley.interval) && dim(A.Shapley.interval)[2] == 3)
|| is.null(A.Shapley.interval)))
stop("wrong Shapley interval constraint matrix")
## check A.interaction.preorder
if (!((is.matrix(A.interaction.preorder)
&& dim(A.interaction.preorder)[2] == 5)
|| is.null(A.interaction.preorder)))
stop("wrong interaction preorder constraint matrix")
## check A.interaction.interval
if (!((is.matrix(A.interaction.interval)
&& dim(A.interaction.interval)[2] == 4)
|| is.null(A.interaction.interval)))
stop("wrong interaction interval constraint matrix")
## check A.inter.additive.partition
if (!((is.numeric(A.inter.additive.partition)
&& sum(levels(factor(A.inter.additive.partition))
== 1:max(A.inter.additive.partition))
== max(A.inter.additive.partition))
|| is.null(A.inter.additive.partition)))
stop("wrong inter-additive partition")
## check epsilon
if (!(is.positive(epsilon) && epsilon <= 1e-3))
stop("wrong epsilon value")
## number of variables without the slack variable z/Epsilon
n.var <- binom.sum(n,k) - 1
## number of monotonicity constraints
n.con <- n*2^(n-1)
## k power set in natural order
subsets <- .C("k_power_set",
as.integer(n),
as.integer(k),
subsets = integer(n.var+1),
PACKAGE="kappalab")$subsets
## monotonicity constraints
A <- .C("monotonicity_constraints",
as.integer(n),
as.integer(k),
as.integer(subsets),
A = integer(n.var * n.con),
PACKAGE="kappalab")$A
A <- matrix(A,n.con,n.var,byrow=TRUE)
A <- cbind(A,rep(0,n.con))
ineqvec <- rep(">=",n.con)
## add the normalization constraint sum a(T) = 1
A <- rbind(c(rep(1,n.var),0),A)
ineqvec <- c("==",ineqvec)
bvec <- c(1,rep(epsilon,n.con))
## add the constraints relative to the preorder of the alternatives
if (!is.null(A.Choquet.preorder)) {
for (i in 1:dim(A.Choquet.preorder)[1]) {
cpc <- Choquet.preorder.constraint(n,k,subsets,
A.Choquet.preorder[i,][1:n],
A.Choquet.preorder[i,][(n+1):(2*n)],
A.Choquet.preorder[i,2*n+1])
A <- rbind(A,c(cpc$A,-1))
ineqvec <- c(ineqvec,">=")
bvec <- c(bvec,cpc$b)
}
}
## add the constraints relative to the preorder of the criteria
if (!is.null(A.Shapley.preorder)) {
for (i in 1:dim(A.Shapley.preorder)[1]) {
spc <- Shapley.preorder.constraint(n,k,subsets,
A.Shapley.preorder[i,1],
A.Shapley.preorder[i,2],
A.Shapley.preorder[i,3])
A <- rbind(A,c(spc$A,-1))
ineqvec <- c(ineqvec,">=")
bvec <- c(bvec,spc$b)
}
}
## add the constraints relative to the importance of the criteria
if (!is.null(A.Shapley.interval)) {
for (i in 1:dim(A.Shapley.interval)[1]) {
sic <- Shapley.interval.constraint(n,k,subsets,
A.Shapley.interval[i,1],
A.Shapley.interval[i,2],
A.Shapley.interval[i,3])
## Sh(i) >= a
A <- rbind(A,c(sic$A,0))
ineqvec <- c(ineqvec,">=")
bvec <- c(bvec,sic$b)
## - Sh(i) >= -b
A <- rbind(A,c(-sic$A,0))
ineqvec <- c(ineqvec,">=")
bvec <- c(bvec,-(sic$b + sic$r))
}
}
## add the constraints relative to the preorder of the interactions
if (!is.null(A.interaction.preorder)) {
for (i in 1:dim(A.interaction.preorder)[1]) {
ipc <- interaction.preorder.constraint(n,k,subsets,
A.interaction.preorder[i,1],
A.interaction.preorder[i,2],
A.interaction.preorder[i,3],
A.interaction.preorder[i,4],
A.interaction.preorder[i,5])
A <- rbind(A,c(ipc$A,-1))
ineqvec <- c(ineqvec,">=")
bvec <- c(bvec,ipc$b)
}
}
## add the constraints relative to the magnitude of the interaction
if (!is.null(A.interaction.interval)) {
for (i in 1:dim(A.interaction.interval)[1]) {
iic <- interaction.interval.constraint(n,k,subsets,
A.interaction.interval[i,1],
A.interaction.interval[i,2],
A.interaction.interval[i,3],
A.interaction.interval[i,4])
## I(ij) >= a
A <- rbind(A,c(iic$A,0))
ineqvec <- c(ineqvec,">=")
bvec <- c(bvec,iic$b)
## I(ij) <= b
A <- rbind(A,c(-iic$A,0))
ineqvec <- c(ineqvec,">=")
bvec <- c(bvec,-(iic$b+iic$r))
}
}
## add the constraints relative to the inter-addtive partition
if (!is.null(A.inter.additive.partition)) {
iapc <- inter.additive.partition.constraint(n,k,subsets,
A.inter.additive.partition)
A <- rbind(A,cbind(iapc$A,0))
bvec <- c(iapc$b,bvec)
ineqvec <- c(ineqvec,rep("==",length(iapc$b)))
}
## lower bound of the Mobius transform
lower.bound <- .C("Mobius_lower_bound",
as.integer(n),
as.integer(k),
as.integer(subsets),
lb = double(n.var),
PACKAGE="kappalab")$lb
# change of variable so that the LP be in standard form
bvec <- bvec - A %*% c(lower.bound,0)
## lpSolve
lp.res <- lp("max",c(rep(0,n.var),1),A,ineqvec,bvec)
print(lp.res)
return(list(solution = Mobius.capacity(c(0,lp.res$solution[1:n.var]+lower.bound),n,k),
value = lp.res$objval,lp.object = lp.res))
}
##############################################################################