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Rough Set Theory and Digraphs

Chiaselotti G., Ciucci D., Gentile T., Infusino F.

Fundamenta Informaticae

2017

Vol. 153, nr 4

291--325

In this paper we apply rough set theory to information tables induced from finite directed graphs without loops and multiples arcs (digraphs). Specifically, we use the adjacency matrix of a digraph as a particular type of information table. In this way, we are able to explore on digraphs the notions of indiscernibility partitions, lower and upper approximations, generalized core, reducts and discernibility matrix. All these ideas will be exemplified on standard digraph families as well on examples from social networks and patterns of flight routes between airports.

Generalizations of Rough Set Tools Inspired by Graph Theory

Chiaselotti G., Ciucci D., Gentile T., Infusino F.

Fundamenta Informaticae

2016

Vol. 148, nr 1/2

207--227

We introduce and study new generalizations of some rough set tools. Namely, the extended core, the generalized discernibility function, the discernibility space and the maximum partitioner. All these concepts where firstly introduced during the application of rough set theory to graphs, here we show that they have an interesting and useful interpretation also in the general setting. Indeed, among other results, we prove that reducts can be computed in incremental polynomial time, we give some conditions in order that a partition coincides with an indiscernibility partition of a given information table and we give the conditions such that a discernibility matrix corresponds to an information table.