poseticDataAnalysis (version 1.0.0)

FuzzySeparation: Fuzzy separation matrix computation

Description

Starting from a poset dominance matrix, computes fuzzy separation matrices by using the t-norm and t-conorm supplied by the user.

Usage

FuzzySeparation(dom, norm, conorm, type, ...)

Value

list of required fuzzy separation matrices.

Arguments

dom

square matrix representing the dominance degree between pairs of poset elements. Columns and rows names of dom are interpreted as the labels of the poset elements. dom can be computed by using functions such as BLSDominance, BubleyByesMRP and ExactMRP.

norm

R-function defining the t-norm

conorm

R-function defining the t-conorm

type

type of fuzzy Separation to be computed. Possible choices are: "symmetric", "asymmetricLower", "asymmetricUpper", "vertical", "horizontal". For details on the definition of symmetric, asymmetric, vertical and horizontal separations see Fattore et al. (2024).

...

additional types of fuzzy separations to be computed. Possible choices are: "symmetric", "asymmetricLower", "asymmetricUpper", "vertical", "horizontal".

References

Fattore, M., De Capitani, L., Avellone, A., and Suardi, A. (2024). A fuzzy posetic toolbox for multi-criteria evaluation on ordinal data systems. Annals of Operations Research, https://doi.org/10.1007/s10479-024-06352-3.

Examples

el <- c("a", "b", "c", "d")

dom_list <- matrix(c(
  "a", "b",
  "c", "b",
  "b", "d"
), ncol = 2, byrow = TRUE)

pos <- POSet(elements = el, dom = dom_list)

BLS <- BLSDominance(pos)

tnorm <- function(x,y){x*y}

tconorm <- function(x,y){x+y-x*y}

FSep <- FuzzySeparation(BLS, norm=tnorm, conorm=tconorm,
            type="symmetric", "asymmetricLower", "vertical")