Digital convex fuzzy hull

Abstract

Problem of defining convexity of a digital region is considered. Definition of DL - (digital line) convexity is proposed, and it is shown to be stronger than the other two definitions, T-(triangle) convexity and L-(line) convexity. In attempt to connect the convexity of digital sets, to the fact that digital set can be a fuzzy set, the notion of convexity of the membership function is introduced. Digital set is placed in (x, y)-plane, and values of the membership function for every centroid of that set is drifted on z-axis, so our consideration is fully and clearly represented in ℝ3. For convexity in (x,y)-plane we chose the DL-convexity (digital line convexity) as the most appropriate for our purpose. For membership function the quasi convexity is chosen. All these notions are introduced, in order to be able to define the digital convex fuzzy hull of a digital fuzzy set.