A Method to Construct Approximate Fuzzy Voronoi Diagram for Fuzzy Numbers of Dimension Two
AbstractIn this paper, we propose an approximate "fuzzy Voronoi" diagram(FVD)for fuzzy numbers of dimension two (FNDT) by designing an extension ofcrisp Voronoi diagram for fuzzy numbers. The fuzzy Voronoi sites are defined asfuzzy numbers of dimension two. In this approach, the fuzzy numbers have a convexcontinuous differentiable shape. The proposed algorithm has two stages: in the firststage we use the Fortune’s algorithm in order to construct a "fuzzy Voronoi" diagramfor membership values of FNDTs that are equal to 1. In the second stage, we proposea new algorithm based on the Euclidean distance between two fuzzy numbers in orderto construct the approximate "fuzzy Voronoi" diagram for values of the membershipof FNDTs that are smaller than 1. The experimental results are presented for aparticular shape, the fuzzy ellipse numbers.
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