Fuzzy filters

Filter Convergence and Fuzzy Topology

“…By similar methods in [12], we can show that (P1) and (P3) hold for convergence (II), (III), respectively. Moreover, it is routine to check that the conditions (P2), (P4) and (P5) hold for convergence (II), (III), (IV), respectively.…”

“…First, we introduce a characterization of a prefilter. (See [12] for details) Definition 4.1. A prefilter F on a set X is an ultrafilter if there is no strictly finer prefilter than F. Theorem 4.8.…”

Hausdorffness on generalized intuitionistic fuzzy filters

“…On the other hand, Lowen [11] introduced the concept of fuzzy filter and defined convergence in a fuzzy topological space which enables us to characterize fuzzy compactness. Many results on fuzzy filter are obtained by De Prada and Saralegui [8,9] and Ramakrishnan and Nayagam [12]. More recently, Mondal and Samanta [10] introduced definitions of GIF sets, generalized intuitionistic fuzzy relations and generalized intuitionistic fuzzy topology and studied some of their properties.…”

Semi-Hausdorff Fuzzy Filters

“…The concept of fuzzy sets was introduced by Zadeh [1]. The theory of fuzzy filters was studied in [2,3]. The notion of fuzzy topological spaces is introduced in [4] and studied in [5,6].…”