ELSEVIER Fuzzy Sets and Systems 87 (1997) 361-368 FUZ2Y sets and systems Fuzzy implicative ideals in BCK-algebras Samy M. Mostafa Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt Received May 1995; revised December 1995 Abstract In this paper, we introduce the concept of fuzzy implicative ideals in BCK-algebras and study some of their properties. © 1997 published by Elsevier Science B.V. Keywords: Implicative ideal; Fuzzy implicative ideal 1. Introduction The concept of a fuzzy set was introduced by Zadeh [15] and was used afterwards by many other authors in various branches of mathematics. Particularly, in the area of fuzzy topology much research has been carried out since. In 1966, Imai and Is6ki [4] introduced the notion of BCK-algebra. Xi [11] applied the concept of fuzzy set to BCK-algebras and gave some properties of it. After that Jun and Meng investigated further properties of fuzzy BCK-a|gebras and fuzzy ideals (see [6-8]). In [11], Meng introduced the notion of implicative ideals. In this paper we introduce the notion of fuzzy implicative ideals of BCK-algebras and obtain some results. 2. Preliminaries Definition 2.1 (Is6ki and Tanaka [5]). An algebraic system (X, *,0) of type (2,0) is called a BCK-algebra if it satisfies the following conditions: (BCK-1) ((x* y)*(x*z))*(z* y)=O, (BCK-2) (x • (x * y)) * y ----0, (BCK-3) x,x=0, (BCK-4) 0*x----0, (BCK-5) x , y = y , x = O implies x ---- y, 0165-0114/97/$17.00 (~) 1997 Published by Elsevier Science B.V. All rights reserved PIIS0165-0114(96)00017-6