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Several fuzzifying topologies on the fuzzy real line | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 23، شماره 4، مهر و آبان 2026، صفحه 21-34 اصل مقاله (400.18 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2026.9973 | ||
| نویسندگان | ||
| F. G. Shi* 1؛ L. Wang2 | ||
| 1School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou, China | ||
| 2School of Mathematical Science, Mudanjiang Normal University, Mudanjiang, Heilongjiang, China | ||
| چکیده | ||
| In [13], three natural fuzzifying topologies are presented on the fuzzy real line. It is proved that the three fuzzifying topologies can be induced respectively by three fuzzifying pseudo-quasi-metrics. In this paper, we present several novel fuzzifying topologies on the fuzzy real line, and discass their relations. | ||
| کلیدواژهها | ||
| Fuzzy number؛ the fuzzy real line؛ fuzzifying topology؛ fuzzifying pseudo-metric | ||
| مراجع | ||
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[1] P. Dwinger, Characterizations of the complete homomorphic images of a completely distributive complete lattice I, Indagationes Mathematicae (Proceedings), 85(4) (1982), 403-414. https://doi.org/10.1016/1385-7258(82) 90034-8 [2] T. E. Gantner, R. C. Steinlage, R. H. Warren, Compactness in fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 62(3) (1978), 547-562. https://doi.org/10.1016/0022-247X(78)90148-8 [3] R. Goetschel, W. Voxman, Topological properties of fuzzy numbers, Fuzzy Sets and Systems, 10(1-3) (1983), 87-99. https://doi.org/10.1016/S0165-0114(83)80107-9 [4] U. H¨ohle, Probabilistsche Metriken auf der Menge nicht negativen verteilungs funktionen, Aequationes Mathematicae, 18 (1978), 345-356. https://doi.org/10.1007/BF03031686 [5] H. L. Huang, F. G. Shi, L-fuzzy numbers and their properties, Information Sciences, 178(4) (2008), 1141-1151. https://doi.org/10.1016/j.ins.2007.10.001 [6] B. Hutton, Normality in fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 50(1) (1975), 74-79. https://doi.org/10.1016/0022-247X(75)90039-6 [7] Z. Jin, C. Shen, T. Rasham, F. G. Shi, Some topologies on the fuzzy real line and their pointwise metrizations, Computational and Applied Mathematics, 45(3) (2025), 104. https://doi.org/10.1007/s40314-025-03460-z [8] I. Kramosil, J. Mich´alek, Fuzzy metric and statistical metric spaces, Kybernetica, 11(5) (1975), 336-344. https: //www.kybernetika.cz/content/1975/5/336/paper.pdf [9] B. Schweizer, A. Sklar, Statistical metric spaces, Pacific Journal of Mathematics, 10(1) (1960), 313-334.
[10] F. G. Shi, Pointwise pseudo-metric on the L-real line, Iranian Journal of Fuzzy Systems, 2(2) (2005), 15-20. https://doi.org/10.22111/ijfs.2005.478 [11] F. G. Shi, (L,M)-fuzzy metric spaces, Indian Journal of Mathematics, 52(2) (2010), 231-250.
[12] F. G. Shi, L-metric on the space of M-fuzzy numbers, Fuzzy Sets and Systems, 399 (2020), 95-109. https: //doi.org/10.1016/j.fss.2020.03.015 [13] F. G. Shi, Fuzzifying pseudo-quasi-metric topologies on the fuzzy real line, Hacettepe Journal of Mathematics and Statistics, 53(2) (2024), 457-470. https://doi.org/10.15672/hujms.1209995 [14] F. G. Shi, Four arithmetic operations of Hutton’s fuzzy numbers, Fuzzy Sets and Systems, 541 (2026), 109942. https://doi.org/10.1016/j.fss.2026.109942 [15] M. S. Ying, Fuzzifying topology based on complete residuated lattice-valued logic (I), Fuzzy Sets and Systems, 56(3) (1993), 337-373. https://doi.org/10.1016/0165-0114(93)90215-4 | ||
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آمار تعداد مشاهده مقاله: 4 تعداد دریافت فایل اصل مقاله: 1 |
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