Fréchet fuzzy metric
Анотація
The aim of this note is to introduce a fuzzy counterpart of the Fréchet distance between curves. We consider both monotonic and non-monotonic case.
Посилання
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3. E.W. Chambers, É. Colin de Verdière, J. Erickson, S. Lazard, F. Lazarus, S. Thite, Homotopic Fréchet distance between curves, or Walking your dog in the woods in polynomial time, Computational Geometry: Theory and Applications, 43 (2009) (3), 295—311, doi:10.1016/j.comgeo.2009.02.008.
4. T. Eiter, H. Mannila, Computing discrete Fréchet distance, Tech. Report CD-TR 94/64, Christian Doppler Laboratory for Expert Systems, TU Vienna, Austria (1994).
5. R. Engelking, Dimension Theory, Amsterdam: North Holland, 1978, 314 p.
6. M. Fréchet, Sur quelques points du calcul fonctionnel, Rend. Circolo Mat. Palermo, 74 (1906), 1–74.
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8. A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets Syst., 90 (1997), 365—368.
9. V. Gregori, S. Romaguera, On completion of fuzzy metric spaces, Fuzzy Sets and Systems, 130 (2002) FRÉCHET FUZZY METRIC 215
10. V. Gregori, S. Romaguera, Characterizing completable fuzzy metric spaces, Fuzzy Sets and Systems, 144 (2004), No3, 411–420.
11. Kamran Alam Khan, Generalized Fuzzy metric Spaces with an application to Colour image filtering, Global Journal of Pure and Applied Mathematics, 13 (2017), No7, 3601–3616.
12. S. Morillas, V. Gregori, G. Peris-Fajarnés, P. Latorre, A new vector median filter based on fuzzy metrics, ICIAR05, Lecture Notes in Computer Science, 3656 (2005), 81–90.
13. N. M. Ralević, D. Karaklić, Neda Pištinjat, Fuzzy metric and its applications in removing the image noise, Soft Computing, 23 (2019), No22, 12049–12061.
14. J. Rodrı́guez-López, S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets and Systems, 147 (2004), 273–283.
15. D. Repovš, A. Savchenko, M. Zarichnyi, Fuzzy Prokhorov metric on the set of probability measures, Fuzzy Sets and Systems, 175 (2011), 96–104.
16. A. Sapena, A contribution to the study of fuzzy metric spaces, Applied General Topology, 2 (2001), No1, 63–75.
17. B. Schweizer, A. Sklar, Associative functions and abstract semigroups, Publ. Math. Debrecen 10 (1963), 69–81.
2. V. Brydun, A. Savchenko, M. Zarichnyi, Fuzzy metrization of the spaces of idempotent measures, European Journal of Mathematics, 6 (2020), 98–109.
3. E.W. Chambers, É. Colin de Verdière, J. Erickson, S. Lazard, F. Lazarus, S. Thite, Homotopic Fréchet distance between curves, or Walking your dog in the woods in polynomial time, Computational Geometry: Theory and Applications, 43 (2009) (3), 295—311, doi:10.1016/j.comgeo.2009.02.008.
4. T. Eiter, H. Mannila, Computing discrete Fréchet distance, Tech. Report CD-TR 94/64, Christian Doppler Laboratory for Expert Systems, TU Vienna, Austria (1994).
5. R. Engelking, Dimension Theory, Amsterdam: North Holland, 1978, 314 p.
6. M. Fréchet, Sur quelques points du calcul fonctionnel, Rend. Circolo Mat. Palermo, 74 (1906), 1–74.
7. A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (1994), 395–399.
8. A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets Syst., 90 (1997), 365—368.
9. V. Gregori, S. Romaguera, On completion of fuzzy metric spaces, Fuzzy Sets and Systems, 130 (2002) FRÉCHET FUZZY METRIC 215
10. V. Gregori, S. Romaguera, Characterizing completable fuzzy metric spaces, Fuzzy Sets and Systems, 144 (2004), No3, 411–420.
11. Kamran Alam Khan, Generalized Fuzzy metric Spaces with an application to Colour image filtering, Global Journal of Pure and Applied Mathematics, 13 (2017), No7, 3601–3616.
12. S. Morillas, V. Gregori, G. Peris-Fajarnés, P. Latorre, A new vector median filter based on fuzzy metrics, ICIAR05, Lecture Notes in Computer Science, 3656 (2005), 81–90.
13. N. M. Ralević, D. Karaklić, Neda Pištinjat, Fuzzy metric and its applications in removing the image noise, Soft Computing, 23 (2019), No22, 12049–12061.
14. J. Rodrı́guez-López, S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets and Systems, 147 (2004), 273–283.
15. D. Repovš, A. Savchenko, M. Zarichnyi, Fuzzy Prokhorov metric on the set of probability measures, Fuzzy Sets and Systems, 175 (2011), 96–104.
16. A. Sapena, A contribution to the study of fuzzy metric spaces, Applied General Topology, 2 (2001), No1, 63–75.
17. B. Schweizer, A. Sklar, Associative functions and abstract semigroups, Publ. Math. Debrecen 10 (1963), 69–81.
Опубліковано
2022-06-27
Як цитувати
Bazylevych, L., Berezsky, O., & Zarichnyi, M. (2022). Fréchet fuzzy metric. Математичні студії, 57(2), 210-215. https://doi.org/10.30970/ms.57.2.210-215
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Авторське право (c) 2022 L. Bazylevych, O. Berezsky, M. Zarichnyi
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