R Under development (unstable) (2023-11-06 r85483 ucrt) -- "Unsuffered Consequences"
Copyright (C) 2023 The R Foundation for Statistical Computing
Platform: x86_64-w64-mingw32/x64

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(kappalab)
Loading required package: lpSolve
Loading required package: quadprog
Loading required package: kernlab
> 
> ## a monotone set function
> mu <- set.func(c(0,1,1,1,2,2,2,3))
> mu
		set.func
{}		0.000000
{1}		1.000000
{2}		1.000000
{3}		1.000000
{1,2}		2.000000
{1,3}		2.000000
{2,3}		2.000000
{1,2,3}		3.000000
> is.monotone(mu)
[1] TRUE
> 
> ## the Mobius representation of a monotone set function
> a <- Mobius.set.func(c(0,1,2,1,3,1,2,1,2,3,1),4,2)
> is.monotone(a)
[1] TRUE
> 
> ## non-monotone examples
> mu <- set.func(c(0,-7:7))
> is.monotone(mu,verbose=TRUE)
Violation of monotonicity constraint between { } and { 1 }. 
Violation of monotonicity constraint between { } and { 2 }. 
Violation of monotonicity constraint between { } and { 3 }. 
Violation of monotonicity constraint between { } and { 4 }. 
[1] FALSE
> a <- Mobius(mu)
> is.monotone(a,verbose=TRUE)
Violation of monotonicity constraint between { } and { 1 }. 
Violation of monotonicity constraint between { } and { 2 }. 
Violation of monotonicity constraint between { } and { 3 }. 
Violation of monotonicity constraint between { } and { 4 }. 
[1] FALSE
> 
> 
> 
> 
> proc.time()
   user  system elapsed 
   0.51    0.06    0.57