Fuzzy Voronoi diagram for disjoint fuzzy numbers of dimension two

In this paper, we introduce “fuzzy Voronoi” diagrams for fuzzy numbers of dimension two FNDT by extension of crisp Voronoi diagrams for fuzzy numbers. The fuzzy Voronoi sites are defined as fuzzy numbers of dimension two. All the operations are defined in FNDT framework. We propose an analytical approach to compute the boundaries of fuzzy Voronoi diagram for pyramidal-shape FNDT.

[1]  William Voxman,et al.  Some remarks on distances between fuzzy numbers , 1998, Fuzzy Sets Syst..

[2]  David G. Kirkpatrick,et al.  A compact piecewise-linear voronoi diagram for convex sites in the plane , 1996, Discret. Comput. Geom..

[3]  Stanislaw Heilpern,et al.  Representation and application of fuzzy numbers , 1997, Fuzzy Sets Syst..

[4]  Madan M. Gupta,et al.  Introduction to Fuzzy Arithmetic , 1991 .

[5]  Michael Hanss,et al.  Applied Fuzzy Arithmetic: An Introduction with Engineering Applications , 2004 .

[6]  Gaëlle Largeteau-Skapin,et al.  Generalized Perpendicular Bisector and exhaustive discrete circle recognition , 2011, Graph. Model..

[7]  Isabelle Bloch,et al.  On fuzzy distances and their use in image processing under imprecision , 1999, Pattern Recognit..

[8]  Xiang Li,et al.  On distance between fuzzy variables , 2008, J. Intell. Fuzzy Syst..

[9]  Evanthia Papadopoulou Critical area computation for missing material defects in VLSIcircuits , 2001, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[10]  A. Kaufmann,et al.  Introduction to fuzzy arithmetic : theory and applications , 1986 .

[11]  Bidyut Baran Chaudhuri,et al.  Some shape definitions in fuzzy geometry of space , 1991, Pattern Recognit. Lett..

[12]  Ahmad Makui,et al.  Fuzzy distance of triangular fuzzy numbers , 2013, J. Intell. Fuzzy Syst..

[13]  D. T. Lee,et al.  The Min-Max Voronoi Diagram of Polygons and Applications in VLSI Manufacturing , 2002, ISAAC.

[14]  Jung-Yuan Kung,et al.  A new dynamic programming approach for finding the shortest path length and the corresponding shortest path in a discrete fuzzy network , 2007, J. Intell. Fuzzy Syst..

[15]  Franz Aurenhammer,et al.  An optimal algorithm for constructing the weighted voronoi diagram in the plane , 1984, Pattern Recognit..

[16]  Debjani Chakraborty,et al.  A theoretical development on a fuzzy distance measure for fuzzy numbers , 2006, Math. Comput. Model..

[17]  Mohammadreza Jooyandeh,et al.  Fuzzy Voronoi Diagram , 2008 .

[18]  Ali Mohades,et al.  Uncertain Voronoi diagram , 2009, Inf. Process. Lett..

[19]  J. J. Buckley,et al.  Fuzzy plane geometry I: Points and lines , 1997, Fuzzy Sets Syst..

[20]  Debjani Chakraborty,et al.  Analytical fuzzy plane geometry I , 2012, Fuzzy Sets Syst..

[21]  J. J. Buckley,et al.  Fuzzy plane geometry II: Circles and polygons , 1997, Fuzzy Sets Syst..

[22]  Chee-Keng Yap,et al.  AnO(n logn) algorithm for the voronoi diagram of a set of simple curve segments , 1987, Discret. Comput. Geom..

[23]  Deok-Soo Kim,et al.  A sweepline algorithm for Euclidean Voronoi diagram of circles , 2006, Comput. Aided Des..

[24]  Mariette Yvinec,et al.  The Voronoi Diagram of Planar Convex Objects , 2003, ESA.

[25]  R. Goetschel,et al.  Elementary fuzzy calculus , 1986 .

[26]  Deok-Soo Kim,et al.  Voronoi diagram of a circle set from Voronoi diagram of a point set: II. Geometry , 2001, Comput. Aided Geom. Des..

[27]  Steven Fortune,et al.  A sweepline algorithm for Voronoi diagrams , 1986, SCG '86.

[28]  Debjani Chakraborty,et al.  A new approach to fuzzy distance measure and similarity measure between two generalized fuzzy numbers , 2010, Appl. Soft Comput..