Convexity is an important concept for the quantitative and qualitative study in operation research which helps to optimize the solution of its problems. Therefore, many authors were interested in this branch and studied this property on sets, cones, hulls and functions. In this paper, we study a modified concept called fuzzy convexity by introducing the notion of convex. M-convex and quasiconvex fuzzy sets, cones and hulls. Some of their relations and topological properties are presented.
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