Abstract
Let S be a subset of R n , and let 0⩽ a⩽1. We call S a-convex if x, y∈S imply a x+(1−a) y∈S . It is incorrectly stated in (Rosenfeld, A., Kak, A.C., 1976. Digital Picture Processing, Academic Press, New York, p. 389; Rosenfeld, A., Kak, A.C., 1982. Digital Picture Processing, second ed. Vol. 2, p. 268) that 1/2-convexity implies convexity. We show that this implication is in fact valid for closed sets and for finite unions of convex sets. We also define fuzzy a-convexity, and show that it implies fuzzy convexity for fuzzy sets whose membership functions are continuous or piecewise constant.
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