ELSEVIER Fuzzy Sets and Systems98 (1998) 383-391 FUIIY sets and systems On fuzzy semi-preopen sets and fuzzy semi-precontinuity S.S. Thakur*, Surendra Singh Department of Applied Mathematics, Government Engineering College, Jabalpur (M.P.) 482011, lndia Received July 1995; revised October 1996 Abstract The purpose of this paper is to introduce and study the concepts of fuzzy semi-preopen sets and fuzzy semi-precontinuous mappings in fuzzy topological spaces. (~) 1998 Elsevier Science B.V. All rights reserved. Keywords: Fuzzy topology; Fuzzy a-open; Fuzzy semi-open; Fuzzy preopen; Fuzzy semi-preopen; Fuzzy semi-continuous; Fuzzy precontinuous; Fuzzy strongly semi-continuous; Fuzzy semi-precontinuous 1. Preliminaries Throughout this paper fts X denotes a fuzzy topological space X and f: X ~ Y means a mapping f from a fuzzy topological space X to a fuzzy topological space Y. Definition 1.1. A fuzzy set 2 in a fts X is called: (a) fuzzy semiopen [2] if 2 ~< C11nt 2, (b) fuzzy a-open [3] if 2~<IntCllnt2, (c) fuzzy preopen [3] if 2~<IntC12. The family of all fuzzy semiopen (resp. fuzzy a-open, fuzzy preopen) sets of a fts X is denoted by FSO(X), (resp. Fa(X), FPO(X)). Definition 1.2. A fuzzy set 2 is called fuzzy semiclosed [2] (resp. fuzzy a-closed [3], fuzzy preclosed [3]) if ~c E FSO(X) (resp. Fa(X), FPO(X)). Remark 1.1. Every fuzzy open set is fuzzy a-open and every fuzzy a-open set is fuzzy semiopen as well as fuzzy preopen, but the separate converses need not be true [3]. Definition 1.3. A mapping f:X ~ Y is called: (a) Fuzzy semi-continuous [2] (resp. fuzzy strongly semi-continuous [3], fuzzy precontinuous [3]), if f-l(2) EFSO(X) (resp. Fa(X), FPO(X)) for every fuzzy open set 2 of Y. * Corresponding author. 0165-0114/98/$19.00 (~) 1998 Elsevier Science B.V. All rights reserved PH SO165-0 114(96)00363-6