A method to construct approximate fuzzy voronoi diagram for fuzzy numbers of dimension two

Abstract

In this paper, we propose an approximate "fuzzy Voronoi" diagram (FVD)for fuzzy numbers of dimension two (FNDT) by designing an extension of crisp Voronoi diagram for fuzzy numbers. The fuzzy Voronoi sites are defined as fuzzy numbers of dimension two. In this approach, the fuzzy numbers have a convex continuous differentiable shape. The proposed algorithm has two stages: in the first stage we use the Fortune's algorithm in order to construct a "fuzzy Voronoi" diagram for membership values of FNDTs that are equal to 1. In the second stage, we propose a new algorithm based on the Euclidean distance between two fuzzy numbers in order to construct the approximate "fuzzy Voronoi" diagram for values of the membership of FNDTs that are smaller than 1. The experimental results are presented for a particular shape, the fuzzy ellipse numbers.