Preclusivity and Simple Graphs

Simple graphs in granular computing

“…In [4] rough sets are used to test bipartiteness of simple undirected graphs. The representation of the graph is different from the one we are using here, indeed the relation at the basis of the rough-set investigation is a preclusive relation (as we also studied in [10]): two vertices are related iff they are connected.…”

“…Let us fix the attribute subset A = {1, 6} and examine the A-granular reference system (P et, A, π A (P et)). In this case we have that π A = 189|25|347 (10). This means that A has three symmetry blocks : {1, 8, 9}, {2, 5, 6} and {3, 4, 7, 10}.…”

“…Specific links between graph theory and rough set theory have been investigated in [4,24,45,44,9,10]. In [4] rough sets are used to test bipartiteness of simple undirected graphs.…”

Micro and macro models of granular computing induced by the indiscernibility relation

“…Taking into account that the granular paradigm [45,46,49,50,62,69,70,74] is permeating much of the new interpretation of information structures (in rough set theory [36,35,48,69,72,75,80,81], generalized rough set theory [3,4,5,34], data mining [20,21,22,32,33,37,51,71], interactive computing [54,55], machine learning [73], computational cognitive science [29], formal concept analysis [26,68,77,78], mathematical morphology [57,58,59,60,61], graph theory [7,8,9,10,11,12,13,14,…”

Rough Sets for n-Cycles and n-Paths

“…In fact, in [22,23,24,25,26] the idea to study any simple undirected graph G as if it were a Boolean information system was developed (in [16] this idea has been also extended to hypergraph theory). The basic tool to connect graphs and Boolean information systems is the adjacency matrix of G, which in [22,23,24,25,26] has been interpreted as the Boolean table of a particular information system. Specifically, in [22,23,24] some graph families, such as the complete graph K n or the complete bipartite graph K p,q , have been broadly studied in terms of information tables.…”