Semi-induced fuzzy topologies

Abstract Induced fuzzy topologies were first introduced by Wong [15] and Weiss [14]. They were studied by Lowen, who called them topologically generated fuzzy topologies [7]. An induced fuzzy topology includes its modification topology. We generalize induced fuzzy topologies to semi-induced fuzzy topologies, viz., those which include their modification topologies. The yet more general fuzzy topologies of structure C are also introduced. The fully stratified fuzzy topological spaces of structure C are precisely the fuzzy neighbourhood spaces of Lowen [4]. In subsequent papers, this relationship will be established and benefited from. The two axioms of semi-induction and structure C hold trivially for crisp fuzzy topologies. We call such axioms (fuzzy) structural axioms in fuzzy topology. In this paper, we analyze the axioms of structure C, semi-induction, and induction. In this context we show how these axioms are linked to the three structural asioms of structures A, B, and D introduced by us in [11]. The basic notions and results pertaining to structures A, B, and D are compiled in the first section. The behaviour of Warren's fuzzy boundary in semi-induced fuzzy topological spaces (fts's for short) is also explained.