# A Method to Construct Approximate Fuzzy Voronoi Diagram for Fuzzy Numbers of Dimension Two

• Dragos Arotaritei Grigore T. Popa” University of Medicine and Pharmacy

### Abstract

In 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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Published
2014-06-15
How to Cite
AROTARITEI, Dragos. A Method to Construct Approximate Fuzzy Voronoi Diagram for Fuzzy Numbers of Dimension Two. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 9, n. 4, p. 389-396, june 2014. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/31>. Date accessed: 07 july 2020. doi: https://doi.org/10.15837/ijccc.2014.4.31.
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### Keywords

approximated fuzzy Voronoi diagram, fuzzy numbers of dimension two, computational geometry, fuzzy arithmetic, bisector median, path planning