tests/lin.prog.capa.ident.R

In kappalab: Non-Additive Measure and Integral Manipulation Functions

library(kappalab)

# example from Marichal and Roubens (cooks)

a <- c(18,15,19)
b <- c(15,18,19)
c <- c(15,18,11)
d <- c(18,15,11)

delta.C <- 0.05
    
Acp <- rbind(c(a,b,delta.C),c(c,d,delta.C))

s <- lin.prog.capa.ident(3,2,A.Choquet.preorder = Acp)

s
m <- s$solution
print(summary(m))

out <- rbind(c(a,mean(a),Choquet.integral(m,a)),
             c(b,mean(b),Choquet.integral(m,b)),
             c(c,mean(c),Choquet.integral(m,c)),
             c(d,mean(d),Choquet.integral(m,d)))

print(out)
    
## some alternatives
a <- c(18,11,18,11,11)
b <- c(18,18,11,11,11)
c <- c(11,11,18,18,11)
d <- c(18,11,11,11,18)
e <- c(11,11,18,11,18)
    
## preference threshold relative
## to the preorder of the alternatives
delta.C <- 1

## corresponing Choquet preorder constraint matrix 
Acp <- rbind(c(d,a,delta.C),
             c(a,e,delta.C),
             c(e,b,delta.C),
             c(b,c,delta.C)
            )

## a Shapley preorder constraint matrix
## Sh(2) - Sh(1) >= delta.S
delta.S <- 0.0
Asp <- rbind(c(2,1,delta.S))

## a Shapley interval constraint matrix
## 0.3 <= Sh(1) <= 0.9 
Asi <- rbind(c(1,0.3,0.9))


## an interaction preorder constraint matrix
## such that I(12) = I(34)
delta.I <- 0.01
Aip <- rbind(c(1,2,3,4,-delta.I),
             c(3,4,1,2,-delta.I))

## an interaction interval constraint matrix
## i.e. -0.20 <= I(12) <= -0.15 
delta.I <- 0.01
Aii <- rbind(c(1,2,-0.2,-0.15))


## a LP 2-additive solution
lin.prog <- lin.prog.capa.ident(5,2,A.Choquet.preorder = Acp)              
m <- lin.prog$solution
m

## the resulting global evaluations
rbind(c(a,mean(a),Choquet.integral(m,a)),
      c(b,mean(b),Choquet.integral(m,b)),
      c(c,mean(c),Choquet.integral(m,c)),
      c(d,mean(d),Choquet.integral(m,d)),
      c(e,mean(e),Choquet.integral(m,e)))

## the Shapley value
Shapley.value(m)

## a LP 3-additive more constrainted solution
lin.prog2 <- lin.prog.capa.ident(5,3,
                                   A.Choquet.preorder = Acp,
                                   A.Shapley.preorder = Asp)
m <- lin.prog2$solution
m
rbind(c(a,mean(a),Choquet.integral(m,a)),
      c(b,mean(b),Choquet.integral(m,b)),
      c(c,mean(c),Choquet.integral(m,c)),
      c(d,mean(d),Choquet.integral(m,d)),
      c(e,mean(e),Choquet.integral(m,e)))
Shapley.value(m)

## a LP 5-additive more constrainted solution
lin.prog3 <- lin.prog.capa.ident(5,5,
                                   A.Choquet.preorder = Acp,
                                   A.Shapley.preorder = Asp,
                                   A.Shapley.interval = Asi,
                                   A.interaction.preorder = Aip,
                                   A.interaction.interval = Aii
				   )

m <- lin.prog3$solution
m
rbind(c(a,mean(a),Choquet.integral(m,a)),
      c(b,mean(b),Choquet.integral(m,b)),
      c(c,mean(c),Choquet.integral(m,c)),
      c(d,mean(d),Choquet.integral(m,d)),
      c(e,mean(e),Choquet.integral(m,e)))
summary(m)