poseticDataAnalysis (version 1.0.0)

FuzzyInBetweenness: Fuzzy in-betweenness array computation

Description

Starting from a poset dominance matrix, computes in-betweenness arrays by using a user supplied t-norm and t-conorm.

Usage

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

Value

a list of three-dimensional arrays, one array for each type of in-betweenness selected by parameter type. The array element of position \([i,j,k]\) represents \(finb_{p_i,p_j,p_k}\) for symmetric in-betweenness, \(finb_{p_i<p_j<p_k}\) for asymmetricLower in-betweenness, and \(finb_{p_k<p_j<p_i}\) for asymmetricUpper in-betweenness.

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 in-betweenness to be computed. Possible choices are: "symmetric", "asymmetricLower", "asymmetricUpper". For details on the definition of symmetric and asymmetric in-betweenness see Fattore et al. (2024).

...

additional types of in-betweenness to be computed. Possible choices are: "symmetric", "asymmetricLower", "asymmetricUpper".

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}

FinB <- FuzzyInBetweenness(BLS, norm=tnorm, conorm=tconorm, type="symmetric", "asymmetricLower")