Abstract
We propose a unified approach to the theory of forward and backward powerset operators induced by fuzzy relations with special attention to the algebraic and topological properties of these operators. On the basis of this theory, we reconsider previous studies done by various authors in the fields of fuzzy rough sets, fuzzy concept analysis and fuzzy mathematical morphology as well as obtain some new results in these areas. In this way we contribute to the development of the theory of fuzzy rough sets, fuzzy concept analysis and fuzzy mathematical morphology on the basis of fuzzy powerset operators induced by fuzzy relations.
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