پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 31 |
| تعداد شمارهها | 834 |
| تعداد مقالات | 8,015 |
| تعداد مشاهده مقاله | 14,852,917 |
| تعداد دریافت فایل اصل مقاله | 9,586,822 |
Relationships between completeness of fuzzy quasi-uniform spaces | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 9، دوره 16، شماره 2، خرداد و تیر 2019، صفحه 97-106 اصل مقاله (202.65 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2019.4545 | ||
| نویسندگان | ||
| Chen Yuan* 1؛ Yueli Yue2 | ||
| 1Department of Mathematics, Ocean University of China, 238 Songling Road, Qingdao, P.R.China. | ||
| 2Department of Mathematics, Ocean University of China, 238 Songling Road, 266100, Qingdao, P.R.China | ||
| چکیده | ||
| In this paper, we give a kind of Cauchy 1-completeness in probabilistic quasi-uniform spaces by using 1-filters. Utilizing the relationships among probabilistic quasi-uniformities, classical quasi-uniformities and Hutton [0, 1]-quasi-uniformities, we show the relationships between their completeness. In fuzzy quasi-metric spaces, we establish the relationships between the completeness of induced probabilistic quasi-uniform spaces and both completeness of induced classical quasi-uniform spaces and induced Hutton [0, 1]-quasi-uniform spaces. | ||
| کلیدواژهها | ||
| probabilistic quasi-uniformity؛ classical quasi-uniformity؛ Hutton [0, 1]-quasi-uniformity؛ 1-filter؛ Cauchy 1-completeness | ||
| مراجع | ||
|
[1] J. Guti´errez Garc´ıa, M. A. De Prada Vicente, Hutton [0, 1]-quasi-uniformities induced by fuzzy (quasi-)metric spaces, Fuzzy Sets and Systems, 157 (2006), 755-766. [2] J. Guti´errez Garc´ıa, On stratified L-valued filters induced by ⊤-filters, Fuzzy Sets and Systems, 157 (2006), 813-819. [3] J. Guti´errez Garc´ıa, M. A. De Prada Vicente, Characteristic values of ⊤-filter, Fuzzy Sets and Systems, 156 (2005), 55-67. [4] J. Guti´errez Garc´ıa, A unified approach to the concept of fuzzy L-uniform space, Ph.D Thesis, 2000. [5] J. Guti´errez Garc´ıa, M. A. De Prada Vicente, S. Romaguera, Completeness of Hutton [0,1]-quasi-uniform spaces, Fuzzy Sets and Systems, 158 (2007), 1791-1802. [6] J. Guti´errez Garc´ıa, J. R. -Lopez, S. Romaguera, On fuzzy uniformities induced by a fuzzy metric space, Fuzzy Sets and Systems, 330 (2018), 52-78. [7] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395-399. [8] A. George, P. Veeramani, Some theorems in fuzzy metric spaces, Journal of Fuzzy Mathematica, 3 (1995), 933-940. [9] V. Gregori, S. Romaguera, On completion of fuzzy metric spaces, Fuzzy Sets and Systems, 130 (2002), 399-404. [10] V. Gregori, A. Lopez-Crevillen, S. Morillas, A. Sapena, On convergence in fuzzy metric spaces, Topology and its Applications, 156 (2009), 3002-3006. [11] V. Gregori, S. Romaguera, Fuzzy quasi-metric spaces, Applied General Topology, 5 (2004), 129-136. [12] B. Hutton, Uniformities on fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 58 (1977), 559-571. [13] U. H¨ohle, A. Sostak, ˘ Axiomatic foundations of fixed-basis fuzzy topology, in: U. H¨ohle, S. E. Rodabaugh (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series, Vol. 3, Kluwer Academic Publishers, Boston, Dordrecht, London, 1999, pp. 123-272 (Chapter 3). [14] U. H¨ohle, Probabilistic metrization of fuzzy uniformities, Fuzzy Sets and Systems, 8(1) (1982), 63-69. [15] U. H¨ohle, Probabilistic topologies induced by L-fuzzy uniformities, Manuscripta Mathematica , 38 (1982), 289-323. [16] I. Kramosil, J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika, 11(5) (1975), 336-344. [17] R. Lowen, Fuzzy uniform spaces, Journal of Mathematical Analysis and Applications, 82 (1981), 370-385. [18] R. Lowen, Completeness, compactness and precompactness in fuzzy uniform spaces: part I, Journal of Mathematical Analysis and Applications, 90 (1982), 563-581. [19] B. Pang, Degrees of separation properties in stratified L-generalized convergence spaces using residual implication, Filomat, 31(20) (2017), 6293-6305. [20] B. Pang, Stratified L-ordered filter spaces, Quaestiones Mathematicae, 40(5) (2017), 661-678. [21] B. Pang, F. G. Shi, Subcategories of the category of L-convex spaces, Fuzzy Sets and Systems, 313 (2017), 61-74. [22] B. Pang, F. G. Shi, Strong inclusion orders between L-subsets and its applications in L-convex spaces, Quaestiones Mathematicae, 41(8) (2018), 1021-1043. [23] J. L. Sieber, W. J. Pervin, Completeness in quasi-uniform spaces, Mathematische Annalen, 158 (1965), 79-81. [24] B. Schweizer, A. Sklar, Statistical metric spaces, Pacific Journal of Mathematics, 10 (1960), 314-334. [25] F. G. Shi, Pointwise quasi-uniformities and p. q. metrics on completely distributive lattices, Acta Mathematica Sinica, 39 (1996), 701-706. [26] Z. Y. Xiu, B. Pang, M-fuzzifying cotopological spaces and M-fuzzifying convex spaces as M-fuzzifying closure spaces, Journal of Intelligent & Fuzzy Systems, 33 (2017), 613-620. [27] Z. Y. Xiu, B. Pang, Base axioms and subbase axioms in M-fuzzifying convex spaces, Journal of Intelligent & Fuzzy Systems, 15(2) (2018), 75-87. [28] Y. Yue, F. G. Shi, On fuzzy pseudo-metric spaces, Fuzzy Sets and Systems, 161 (2010), 1105-1106. [29] Y. Yue, J. Fang, Uniformities in fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 12 (2015), 43-57. [30] Y. Yue, J. Fang, Completeness in probabilistic quasi-uniform space, Fuzzy Sets and Systems, Available online 7 August 2018. [31] W. Yao, L. X. Lu, Analogizing Hutton’s quasi-uniformities for complete lattices and extending Shi’s quasiuniformities to closed set lattices, Fuzzy Sets and Systems, 160 (2009), 1233-1244. [32] D. Zhang, A comparison of various uniformities in fuzzy topology, Fuzzy Sets and Systems, 140 (2003), 399-422. [33] D. Zhang, Uniform environments as a general framework for metrics and uniformities, Fuzzy Sets and Systems, 159 (2008), 559-572. | ||
|
آمار تعداد مشاهده مقاله: 1,108 تعداد دریافت فایل اصل مقاله: 508 |
||