| Title of paper:
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An intuitionistic fuzzy estimation of the area of 2D–figures
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| Author(s):
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| Evgeniy Marinov
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| Bioinformatics and Mathematical Modelling Department, IBPhBME - Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str., block 105, Sofia 1113, Bulgaria
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| evgeni.marinov@gmail.com
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| Emilia Velizarova
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| Institute of Forest Research, Bulgarian Academy of Sciences, 132, St. Kliment Ohridski Blvd, Sofia 1756, Bulgaria
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| velizars@abv.bg
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| Krassimir Atanassov
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| Bioinformatics and Mathematical Modelling Department, IBPhBME - Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str., block 105, Sofia 1113, Bulgaria
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| krat@bas.bg
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| Presented at:
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9th International Workshop on Intuitionistic Fuzzy Sets, 8 October 2013, Banská Bystrica, Slovakia
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| Published in:
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"Notes on Intuitionistic Fuzzy Sets", Volume 19, 2013, Number 2, pages 57-70
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| Download:
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 PDF (124 Kb, File info)
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| Abstract:
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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.
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| Keywords:
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Square hull, Inner and outer polygon, Intuitionistic fuzzy estimation.
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| AMS Classification:
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03E72
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| References:
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- Atanassov, K. Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Verlag Heidelberg, 1999.
- Atanassov, K. On Intuitionistic Fuzzy Sets Theory, Springer-Verlag, Berlin, 2012.
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- Munkres, J. Topology, 2nd ed., Prentice Hall, 2000.69
- 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.
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