Affiliations: Department of Applied Mathematics, Hanyang University, Ahnsan, Korea | Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul, Korea | Department of Mathematics, University of Alabama, Tuscaloosa, AL, USA
Note: [] Corresponding author. Hee Sik Kim, Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea. Tel.: +82 2 2290 0897; Fax: +82 2 2281 0019; E-mail: [email protected]
Abstract: In this paper, for a given groupoid (X, *) and a relation R on X we consider a related structure LFRX = {< x, y, z > ∈ X3 | xRy, yRz}, and we discuss three different types on LFRX, and we construct a linear fuzzy real BCK-algebra (LF≤X, $\ominus$, ε(0)) and a new BCK-algebra (LF≤X, $\oast$, ε(0)) from a BCK-algebra (X, *, 0).
Keywords: Linear fuzzy real number, linear fuzzy real BCK-algebra, BCK-algebra, Bin(X), poset, additive type, subtractive type, reverse subtractive type
