Mathematical models and computer simulation experiment
Ohanyan V.K., Bardakhchyan V.G., Simonyan A.R., Ulitina E.I. —
Fuzzification of convex bodies in Rn
// Software systems and computational methods.
– 2019. – ¹ 2.
– P. 1 - 10.
DOI: 10.7256/2454-0714.2019.2.29894 URL: https://en. nbpublish.com/library_read_article.php?id=29894
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The paper is dedicated to the generalization of Matheron’s theorem about covariogram to the case where possible estimation error occurs, modelled by fuzzification of convex bodies. The classic case of identification of convex bodies does not consider the cases when input information and measurement contain error term. This is general issue when applying line segment distributions to recover covariogram and later the body itself.
We define a body and ask what result we will get for length distribution for the given fuzzy body. Through this procedure we generalize Matheron’s theorem for this case. We extensively use fuzzy statistics and fuzzy random variables to extend convex bodies and length distribution functions to the fuzzy case. We use several properties of fuzzy numbers and fuzzy calculus techniques (mainly Aumann integration).
We introduce generalized fuzzy distribution to apply them in a general setting of fuzzy convex bodies. Fuzzy convex bodies are defined by adding to the convex body and subtracting (in Hukuhara sense) from its fuzzy numbers in Rn. Then the generalization of Matheron’s theorem for a fuzzy case is derived, based on fuzzy function calculus techniques. Fuzzy convex bodies can be seen as a collection of convex bodies. We introduced fuzzy covariogram based on fuzzy convex bodies.
Matheron’s theorem, Ñonvex body, Fuzzy distribution, Fuzzy covariogram, Integral geometry, Aumann integration, Gaussian field, V-lines, Åstimation error, Hukuhara Differentiability
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