Abstract
The paper presents essential connections between fuzzifying convexities, fuzzifying interval operators and fuzzy pre-orders. Firstly, we study the relationship between fuzzifying convex structures and fuzzifying interval operators on a universal set. Secondly, we show that there exists a connection between based-point fuzzy orders and geometric fuzzifying interval operators on fuzzy partially ordered sets. Finally, we establish a connection between fuzzifying convexities and fuzzy pre-orders.
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