اخبار و اعلانات
آمار
| تعداد نشریات | 26 |
| تعداد شماره‌ها | 552 |
| تعداد مقالات | 5,709 |
| تعداد مشاهده مقاله | 7,972,603 |
| تعداد دریافت فایل اصل مقاله | 5,355,163 |
$L-$ordered Fuzzifying Convergence Spaces | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 11، دوره 9، شماره 2، تابستان 2012، صفحه 147-161 اصل مقاله (419.94 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2012.218 | ||
| نویسندگان | ||
Wenchao Wu  ؛ Jinming Fang
| ||
| Department of Mathematics, Ocean University of China, 266100 Qing- dao, P. R. China | ||
| چکیده | ||
| Based on a complete Heyting algebra, we modify the definition of lattice-valued fuzzifying convergence space using fuzzy inclusion order and construct in this way a Cartesian-closed category, called the category of $L-$ordered fuzzifying convergence spaces, in which the category of $L-$fuzzifying topological spaces can be embedded. In addition, two new categories are introduced, which are called the category of principal $L-$ordered fuzzifying convergence spaces and that of topological $L-$ordered fuzzifying convergence spaces, and it is shown that they are isomorphic to the category of $L-$fuzzifying neighborhood spaces and that of $L-$fuzzifying topological spaces respectively. | ||
| کلیدواژه‌ها | ||
| $L-$fuzzifying topology؛ $L-$ordered fuzzifying convergence structure؛ $L-$filter؛ Cartesian-closed category؛ Reflective subcategory | ||
| مراجع | ||
|
bibitem{1} H. Boustique, R. N. Mohapatra and G. Richardson, {it Lattice-valued fuzzy interior operators}, Fuzzy Sets and Systems, {bf 160} (2009), 2947-2955. bibitem{2} H. Boustique and G. Richardson, {it A note on regularity}, Fuzzy Sets and Systems, {bf 162} (2011), 64-66. bibitem{3} J. Fang, {it Stratified $L-$ordered convergence structures}, Fuzzy Sets and Systems, {bf 161} (2010), 2130-2149. bibitem{4} P. V. Flores, R. N. Mohapatra and G. Richardson, {it Lattice-valued spaces: fuzzy convergence}, Fuzzy Sets and Systems, {bf 157} (2006), 2706-2714. bibitem{5} P. V. Flores and G. Richardson, {it Lattice-valued convergence: diagonal axioms}, Fuzzy Sets and Systems, {bf 159} (2008), 2520-2528. bibitem{6} U. H"{o}hle, {it Characterization of $L-$topologies by $L-$valued neighborhoods}, Chapter 5, In: Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series, (U. H"{o}hle, S. E. Rodabaugh, eds.), Kluwer Academic Publishers, Boston, Dordrecht, London, {bf3} (1999), 389-432. bibitem{7} U. H"{o}hle and A. P. v{S}ostak, {it Axiomatic foundations of fixed-basis fuzzy topology}, In: Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series, (U. H"{o}hle, S. E. Rodabaugh, eds.), Kluwer Academic Publishers, Boston, Dordrecht, London, {bf3} (1999), 123-173. bibitem{8} G. J"{a}ger, {it A category of $L-$fuzzy convergence spaces}, Quaestiones Mathematicae, {bf 24} (2001), 501-517. bibitem{9} G. J"{a}ger, {it Subcategories of lattice-valued convergence spaces}, Fuzzy Sets and Systems, {bf 156} (2005), 1-24. bibitem{10} G. J"{a}ger, {it Pretopological and topological lattice-valued convergence spaces}, Fuzzy Sets and Systems, {bf 158} (2007), 424-435. bibitem{11} G. J"{a}ger, {it Fischer's diagonal condition for lattice-valued convergence spaces}, Quaestiones Mathematicae, {bf 31} (2008), 11-25. bibitem{12} R. Lowen, {it Convergence in fuzzy topological spaces}, Gen. Top. Appl., {bf 10} (1979), 147-160. bibitem{13} K. C. Min, {it Fuzzy limit spaces}, Fuzzy Sets and Systems, {bf 32} (1989), 343-357. bibitem{14} L. Xu, {it Characterizations of fuzzifying topologies by some limit structures}, Fuzzy Sets and Systems, {bf 123} (2001), 169-176. bibitem{15} W. Yao, {it On many-valued stratified $L-$fuzzy convergence spaces}, Fuzzy Sets and Systems, {bf 159} (2008), 2503-2519. bibitem{16} W. Yao, {it On $L-$fuzzifying convergence spaces}, Iranian Journal of Fuzzy Systems, {bf 6}textbf{(1)} (2009), 63-80. bibitem{17} M. S. Ying, {it A new approach to fuzzy topology (I)}, Fuzzy Sets and Systems, {bf 39} (1991), 303-321. bibitem{18} D. Zhang, {it On the reflectivity and coreflectivity of $L-$fuzzifying topological spaces in $L-$topological spaces}, Acta Mathematica Sinica (English Series), {bf 18}textbf{(1)} (2002), 55-68. bibitem{19} D. Zhang, {it $L-$fuzzifying topologies as $L-$topologies}, Fuzzy Sets and Systems, {bf 125} (2002), 135-144. bibitem{20} D. Zhang and L. Xu, {it Categories isomorphic to bf FNS}, Fuzzy Sets and Systems, {bf 104} (1999), 373-380. | ||
|
آمار تعداد مشاهده مقاله: 2,184 تعداد دریافت فایل اصل مقاله: 1,066 |
||
