R/ls.ranking.capa.ident.R

In kappalab: Non-Additive Measure and Integral Manipulation Functions

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#
# Copyright  2005 Michel Grabisch, Ivan Kojadinovic, and Patrick Meyer
#
# Ivan.Kojadinovic@polytech.univ-nantes.fr
#
# This software is a package for the statistical system GNU R:
# http://www.r-project.org 
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## Least squares ranking capacity identification

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ls.ranking.capa.ident <- function(n, k, C, rk, d,
                                A.Shapley.preorder = NULL,
                                A.Shapley.interval = NULL,
                                A.interaction.preorder = NULL,
                                A.interaction.interval = NULL,
                                A.inter.additive.partition = NULL,
                                sigf = 5,
                                maxiter = 20,
				epsilon = 1e-6) {
    
    ## check n and k
    if (!(as.integer(n) == n && k %in% 1:n))## check n and k
        stop("wrong arguments")

    ## number of alternatives
    n.var.alt <- dim(C)[1]
    
    ## check C
    if (!(is.matrix(C) && dim(C)[2] == n)) 
        stop("wrong criteria matrix")
    
    ## check rk
	if (!(is.matrix(rk) && dim(rk)[2] == 2)) 
        stop("wrong criteria matrix")

    
    Integral <- "Choquet"

    ## 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 linked to the capacity
    n.var.a <- binom.sum(n,k) - 1

    ## total number of variables
    n.var <- n.var.a + n.var.alt

    ## number of monotonicity constraints
    n.con <- n*2^(n-1)

    ## infinity value
    infty  <- 1000

     
    ## k power set in natural order
    subsets <-  .C("k_power_set", 
                   as.integer(n),
                   as.integer(k),
                   subsets = integer(n.var.a+1),
                   PACKAGE="kappalab")$subsets

        
    ## monotonicity constraints
    A <- .C("monotonicity_constraints", 
            as.integer(n), 
            as.integer(k),
            as.integer(subsets),
            A = integer(n.var.a * n.con),
            PACKAGE="kappalab")$A


    A <- matrix(A,n.con,n.var.a,byrow=TRUE)
    A <- cbind(A,matrix(0,n.con,n.var.alt))

    ## add the normalization constraint sum a(T) = 1
    A <- rbind(c(rep(1,n.var.a),numeric(n.var.alt)),A)
    b <- c(1,rep(epsilon,n.con))
    r <- c(0,rep(1,n.con))
 
    ## a part of the objectif matrix R'R
    obj <-  .C("k_additive_objectif", 
             as.integer(n),
             as.integer(k),
             as.integer(subsets),
             as.integer(Integral == "Choquet"),
             as.double(t(C)),
             as.integer(n.var.alt),
             R = double(n.var.alt * n.var.a),
             l = double(n.var.a),
             u = double(n.var.a), 
             PACKAGE="kappalab")

    Rmat <- cbind(matrix(obj$R,n.var.alt,n.var.a,byrow=TRUE),
    diag(-1,n.var.alt,n.var.alt))
    Dmat <- t(Rmat) %*% Rmat
    
    ## constraints relative to the order on the prototypes

	for (i in 1:dim(rk)[1]){
		proto.constraint <- numeric(n.var.alt)
		

		proto.constraint[which(rownames(C)==rk[i,2])]=-1
		proto.constraint[which(rownames(C)==rk[i,1])] = 1
		A <- rbind(A, c(numeric(n.var.a), proto.constraint))
		b <- c(b, d)
		r <- c(r, infty - (-infty) - d)
	}



     ## 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])
            
          spc$A <- c(spc$A, numeric(n.var.alt))
          A <- rbind(A, spc$A)
          b <- c(b,spc$b)
          r <- c(r,spc$r)
        }	
    }

 
    ## add the constraints relative to the absolute 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])

            sic$A <- c(sic$A,numeric(n.var.alt))
            
            A <- rbind(A,sic$A)
            b <- c(b,sic$b)
            r <- c(r,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])
            ipc$A <- c(ipc$A,numeric(n.var.alt))
            
            A <- rbind(A,ipc$A)
            b <- c(b,ipc$b)
            r <- c(r,ipc$r)	
        }	
    }

    ## 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])

            iic$A <- c(iic$A, numeric(n.var.alt))
            A <- rbind(A,iic$A)
            b <- c(b,iic$b)
            r <- c(r,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)

        zeros <- matrix(numeric(n.var.alt * dim(iapc$A)[1]),dim(iapc$A)[1],n.var.alt)

        iapc$A <- cbind(iapc$A, zeros)
        A <- rbind(A,iapc$A)
        b <- c(b,iapc$b)
        r <- c(r,iapc$r)
    }


    ## the global scores on the alternatives can vary between
    ## -infinity and +infinity
    
    l<-c(obj$l,rep(-infty,n.var.alt))
    u<-c(obj$u,rep(+infty,n.var.alt))
    
    ## ipop quadratic program solver
    qp <- ipop(matrix(0,n.var,1), 
     		Dmat,
		A,
		matrix(b),
		matrix(l),
		matrix(u),
		matrix(r),
		sigf,
		maxiter,
		verb=0)
      
    ## solution   
	
	Choquet.C <- numeric(dim(C)[1])
	for (i in 1:(dim(C)[1]))
		Choquet.C[i] <- Choquet.integral(Mobius.capacity(c(0,qp@primal[1:n.var.a]),n,k),C[i,])

	rk.C <- as.matrix(rank(round(Choquet.C,4), ties.method="min"))

	rownames(rk.C) <- rownames(C)

	colnames(rk.C) <- "rank"

	return(list(solution = Mobius.capacity(c(0,qp@primal[1:n.var.a]),n,k),
		glob.eval = qp@primal[(n.var.a+1):(n.var.a+n.var.alt)],
		how = qp@how,
		rk.C = rk.C,
		Choquet.C = Choquet.C))
} 

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