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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/10828

Title: On the category of $L$-fuzzy neighborhood groups and its connections with various categories of $L$-convergence groups
Authors: Jawaher Al-Mufarrij
T. M. G. Ahsanullah
Keywords: U. Hohle
A. P. Sostak
S. E. Rodabaugh
Issue Date: 2010
Publisher: International Conference on Topology and its Application ,Nafpaktos
Citation: Greece, June 26-30, 2010; Abstract Accepted.)
Abstract: Motivated by the notion of $L$-fuzzy neighborhood system attributed to U. Hohle and A. P. Sostak [Axiomatic foundations of fixed basis fuzzy topology, in: Mathematics of Fuzzy Sets: Topology, Logic and Measure Theory, Edited by U. Hohle and S. E. Rodabaugh, Kluwer Academic Publishers, Dordrecht, 1999], we introduce for a frame $L$, categories S$L$-FNeighGrp, of stratified $L$-fuzzy neighborhood groups, and S$L$-FIntGrp, of stratified $L$-fuzzy interior groups. We show that these two categories are isomorphic; some basic facts along with some characterization theorems are presented. Considering the notion of stratified $L$-pre-topological convergence space due to H. Boustique, R. N. Mohapatra and G. Richardson [Lattice-valued fuzzy interior opeators, International J. Fuzzy Sets and Systems 160(2009), 2947-2955], we show that the category S$L$-P-TopConvGrp, of stratified $L$-pre-topological convergence groups, is isomorphic to the category S$L$-FNeighGrp. Also, considering a full subcategory S$L$-FNeighGrp', we show that this category is isomorphic to a subcategory of the category S$L$-GConvGrp, of stratified $L$-generalized convergence groups [T. M. G. Ahsanullah and Jawaher Al-Mufarrij, Frame-valued stratified generalized convergence groups, Quaest. Math. 31(2008), 279-302]; the key item of this category is the notion of stratified $L$-generalized convergence structure initiated by G. Jager [A category of $L$-fuzzy convergence spaces, Quaest. Math. 24(2001), 501-517]. Finally, we propose two more categories HS-S$L$-FFil, of Hohle-Sostak straified $L$-fuzzy filter spaces, and HS-S$L$-FFilGrp, of stratified $L$-fuzzy filter gropus, and discuss some of their features.
URI: http://hdl.handle.net/123456789/10828
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