© Hindawi Publishing Corp. FUZZY BCI-SUBALGEBRAS WITH INTERVAL-VALUED MEMBERSHIP FUNCTIONS

Abstract. The purpose of this paper is to define the notion of an interval-valued fuzzy BCI-subalgebra (briefly, an i-v fuzzy BCI-subalgebra) of a BCI-algebra. Necessary and suf-ficient conditions for an i-v fuzzy set to be an i-v fuzzy BCI-subalgebra are stated. A way to make a new i-v fuzzy BCI-subalgebra from old one is given. The images and inverse images of i-v fuzzy BCI-subalgebras are defined, and how the images or inverse images of i-v fuzzy BCI-subalgebras become i-v fuzzy BCI-subalgebras is studied. 2000 Mathematics Subject Classification. Primary 06F35, 03B52. 1. Introduction. The notion of BCK-algebras was proposed by Iami and Iséki in 1966. In the same year, Iséki [2] introduced the notion of a BCI-algebra which is a gen-eralization of a BCK-algebra. Since then numerous mathematical papers have been written investigating the algebraic properties of the BCK/BCI-algebras and their re-lationship with other universal structures including lattices and Boolean algebras