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We show that a definition of convexity based on the convexity of the score function does not guarantee preservation of convexity under intersections and provide a concept of convexity for hesitant fuzzy sets without this backdraw. We study the relationship between convex hesitant fuzzy sets and convex rough sets as their cuts.

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Starting with a collection of closure systems each of which is associated to an element of a given set X, we construct a lattice L and an L-fuzzy relation on X, such that its fuzzy blocks are precisely the given closure systems.

No abstract