pairwise_mass: Computes the relational representation

Description

pairwise_mass computes the relational representation of a credal partition, as defined in Denoeux et al (2018).

Usage

pairwise_mass(clus)

Value

A list with three "dist" objects:

M0: The masses assigned to the assumption that each pair of object (i,j) do not belong to the same class.
M1: The masses assigned to the assumption that each pair of object (i,j) belongs to the same class.
Me: The masses assigned to the empty set, for each pair of object (i,j).

Arguments

clus: A credal partition (a matrix of n rows and f columns, where n is the number of objects and f is the number of focal sets).

Details

Given a credal partition, we can compute, for each pair of objects, a "pairwise mass function" on a frame \(\Theta=\{s,\neg s\}\), where \(s\) means that the two objects belong to the same cluster, and \(\neg s\) is the negation of \(s\). Function pairwise_mass compute these pairwise mass functions for all object pairs. The result is return as a list with "dist" objects containing the masses of each of the two elements of \(\Theta\), and the masses on the empty set.

References

T. Denoeux, S. Li and S. Sriboonchitta. Evaluating and Comparing Soft Partitions: an Approach Based on Dempster-Shafer Theory. IEEE Transactions on Fuzzy Systems, 26(3):1231-1244, 2018.

Examples

Run this code

## Butterfly data
data(butterfly)
clus<-kevclus(butterfly,c=2)
P<-pairwise_mass(clus)

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