Issue:An intuitionistic fuzzy estimation of the area of 2D–figures

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Title of paper: An intuitionistic fuzzy estimation of the area of 2D–figures
Author(s):
Evgeni Marinov
Bioinformatics and Mathematical Modelling Department, IBPhBME - Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str., block 105, Sofia 1113, Bulgaria
evgeni.marinovAt sign.pnggmail.com
Emilia Velizarova
Institute of Forest Research, Bulgarian Academy of Sciences, 132, St. Kliment Ohridski Blvd, Sofia 1756, Bulgaria
velizarsAt sign.pngabv.bg
Krassimir Atanassov
Bioinformatics and Mathematical Modelling Department, IBPhBME - Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str., block 105, Sofia 1113, Bulgaria
kratAt sign.pngbas.bg
Presented at: 9th International Workshop on Intuitionistic Fuzzy Sets, 8 October 2013, Banská Bystrica, Slovakia
Published in: "Notes on IFS", Volume 19, 2013, Number 2, pages 57-70
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Abstract: An iterative procedure is proposed, starting from an initial grid-step and ending up with a smaller grid-step – small enough to be able to build the square hull for the given iteration. We propose in this paper also a formula for intuitionistic fuzzy estimation for the area surrounded by a continuous simple closed curve in the real 2D space. Therefore, this is a numerical method allowing to program the algorithm in any procedural language. The iterative process stops when a small enough limit between the upper and lower estimation has been reached.
Keywords: Square hull, Inner and outer polygon, Intuitionistic fuzzy estimation.
AMS Classification: 03E72
References:
  1. Atanassov, K. Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Verlag Heidelberg, 1999.
  2. Atanassov, K. On Intuitionistic Fuzzy Sets Theory, Springer-Verlag, Berlin, 2012.
  3. Atanassov, K., V. Tasseva, E. Szmidt, J. Kacprzyk. On the geometrical interpretations of the intuitionistic fuzzy sets. Issues in the Representation and Processing of Uncertain and Imprecise Information. Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets, and Related Topics (Eds. Atanassov K., J. Kacprzyk, M. Krawczak, E. Szmidt), EXIT, Warsaw, 2005.
  4. Munkres, J. Topology, 2nd ed., Prentice Hall, 2000.69
  5. Szmidt, E., J. Baldwin. New similarity measure for intuitionistic fuzzy set theory and mass assignment theory. Notes on Intuitionistic Fuzzy Sets, Vol. 9, 2003, No. 3, 60–76.
  6. Szmidt, E., J. Baldwin. Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems, Vol. 114, 2000, No. 3, 505–518.
  7. Zadeh L. A. Fuzzy sets. Information and Control, Vol. 8, 1965, No. 3, 338–353.
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