ON FUZZY CLOSED MAPS IN FUZZY BICLOSURE SPACES U. D. TAPI AND R. NAVALAKHE Abstract. The purpose of this paper is to introduce the notions of fuzzy closed map and fuzzy open map in fuzzy biclosure spaces and investigate some of their properties . 1. Introduction With the introduction of fuzzy sets by Zadeh [7] and fuzzy topology by Chang [3], the theory of fuzzy topological spaces was subsequently developed by several authors by considering the basic concepts of general topology. Closure spaces were introduced by E.  Cech [2]. The notions of closure system and closure operators are very useful tools in several areas of mathematics playing an important role in the study of topological spaces , Boolean algebra , convex sets etc. Fuzzy closure spaces have been introduced and studied as a generalization of closure spaces, by A.S Mashhour and M.H Ghanim [4]. Recently, Boonpok [1] introduced the notion of biclosure space, as a space equipped with two arbitrary closure operators. He extended some of the standard results of separation axioms from closure spaces to biclosure spaces. Thereafter a large number of papers have been written to generalize the concept of closure space to biclosure space. The authors [6] have introduced the notion of fuzzy biclosure spaces and generalized the concept of fuzzy closure space to fuzzy biclosure space. In this paper we introduce the concepts of fuzzy closed map and fuzzy open map in fuzzy biclosure spaces and investigate some properties of these maps. 2. Preliminaries Let X be an arbitrary set, I = [1; 0] and I X be a family of all fuzzy subsets of X. For a fuzzy set A of X; cl(A); int(A) and 1  A will denote the closure of A, the interior of A and the complement of A respectively whereas the constant fuzzy sets taking on the values 0 and 1 on X are denoted by 0 X and 1 X respectively. Denition 2.1. [4] Let X be a nonempty set. A function u : I X ! I X is said to be a fuzzy closure operator for X, if it satises the following three conditions : (i) u =  2000 Mathematics Subject Classication. 54A40. Key words and phrases. Fuzzy closure operator, Fuzzy closure space, Fuzzy biclosure space, Fuzzy closed map, Fuzzy open map. 249