Alternative ways of creating PowerRelation objects.

## Usage

as.PowerRelation(x, ...)

# S3 method for character
as.PowerRelation(x, ...)

# S3 method for list
as.PowerRelation(x, ..., comparators = c(">"))

## Arguments

x

An object

...

comparators

Vector of ">" or "~" characters

## Using a character string

The same way a power relation $$\succsim$$ may be represented in literature (or printed by an PowerRelation object), a simple string containing letters, numbers, > or ~ can be used to input a new power relation.

Every special character is ignored, with the exception of $$\succsim$$ ("\u227B") and $$\sim$$ ("\u223C").

Every letter or number is assumed to be an individual element. "abc > ac" therefore would represent two coalitions, the first one of size 3 with the elements a, b, and c. This method does not allow for elements to be entered that are supposed to be multiple characters long.

An empty coalitions can be simply left blank (i.e., "abc > ~ ac"), though it is often clearer if curly braces are used to indicate such (i.e., "abc > {} ~ ac").

## Using a list

Create a PowerRelation object with an unnested list of coalition vectors.

By default, a linear order is assumed on the coalitions. I.e., if it is given list(c(1,2),1,2), these three coalitions are put into their own equivalence class, producing 12 > 1 > 2.

The comparators in-between can be adjusted to indicate whether the relation between two coalitions is that of strict preference > or indifference ~.

## Examples

# Using character strings
as.PowerRelation("abc > ab > ({} ~ c) > (a ~ b ~ ac) > bc")
#> abc > ab > ({} ~ c) > (a ~ b ~ ac) > bc
# abc > ab > ({} ~ c) > (a ~ b ~ ac) > bc

# using createPowerset(), then shifting coalitions up and down using Alt+Up and Alt+Down
if(interactive()) {
createPowerset(1:2, result = "copy")
}
as.PowerRelation("
12
> 1
~ {}
> 2
")
#> 12 > (1 ~ {}) > 2

# Using lists
as.PowerRelation(list(c(1,2), 2, c(), 1))
#> 12 > 2 > {} > 1
# 12 > 2 > {} > 1

as.PowerRelation(list(c(1,2), 2, c(), 1), comparators = c("~", ">", ">"))
#> (12 ~ 2) > {} > 1
# (12 ~ 2) > {} > 1

# the length of comparators doesn't necessarily matter.
# If comparators are missing, the existing ones are simply repeated...
as.PowerRelation(list(c(1,2), 2, c(), 1), comparators = "~")
#> (12 ~ 2 ~ {} ~ 1)
# (12 ~ 2 ~ {} ~ 1)

as.PowerRelation(list(c(1,2), 2, c(), 1), comparators = c("~", ">"))
#> (12 ~ 2) > ({} ~ 1)
# (12 ~ 2) > ({} ~ 1)

# ... or the rest is cut off
as.PowerRelation(list(c(1,2), 2, c(), 1), comparators = c("~", ">", "~", "~", ">"))
#> (12 ~ 2) > ({} ~ 1)
# (12 ~ 2) > ({} ~ 1)