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Erschienen in:
16.08.2016 | Original Article
On relationship between generalized rough multisets and multiset topologies
Erschienen in: International Journal of Machine Learning and Cybernetics | Ausgabe 6/2017
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Abstract
The purpose of this paper is to investigate the relationship between multiset topology (M-topology) and generalized rough multiset induced by multiset relation. The notion of transitive closure of a relation is proposed in multiset context. The notable results we establish here are (1) any serial multiset relation induce an M-topology (2) any reflexive multiset relation R and its transitive closure t(R) induce the same M-topology, i.e., \(\tau (R)=\tau (t(R))\). The interior and closure operators of the M-topology \(\tau (R)\) is obtained and discuss their relationship with multiset relation R, when R is a reflexive multiset relation. On the other part, we consider the case when R is a tolerance multiset relation.