FuzzySeparationProbabilistic: Fuzzy Separation matrix computation with Product t-norm and Probabilistic-sum t-conorm

Description

Starting from a poset dominance matrix, computes fuzzy Separation matrices by using Product t-norm and Probabilistic-sum t-conorm

Usage

FuzzySeparationProbabilistic(dom, type, ...)

Value

list of required fuzzy separation matrices.

Arguments

dom: square matrix representing the dominance degrees 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.
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

Run this code

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)

FSep <- FuzzySeparationProbabilistic(BLS, type="symmetric", "asymmetricLower", "vertical")

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