Flow-based tolerance rough sets for pattern classification

A valued outranking graph comprising four nodes and arcs between x1 and x2, x2 and x3, x3 and x4 is illustrated in Fig. 1, in which each node corresponds to a pattern. As depicted in Figs. 2 and 3, the leaving flow ϕ+(xi) and the entering flow ϕ−(xi) of xi are generated. This paper contributes to propose a novel flow-based TRS (FTRS) which uses preference information expressed by flows among patterns to measure the similarity between any two patterns.