(Hindawi, 2014) Ahn, Sun Shin; Kim, Young Hee; Neggers, J.; Dongguk University; Chungbuk National University; University of Alabama Tuscaloosa
The notion of a fuzzy upper bound over a groupoid is introduced and some properties of it are investigated. We also define the notions of an either-or subset of a groupoid and a strong either-or subset of a groupoid and study some of their related properties. In particular, we consider fuzzy upper bounds in Bin(X), where Bin(X) is the collection of all groupoids. Finally, we define a fuzzy-d-subset of a groupoid and investigate some of its properties..
(Wiley, 2001) Neggers, Joseph; Ahn, Sun Shin; Kim, Hee Sik
We introduce a new notion, called a Q-algebra, which is a generalization of the idea of BCH /BCI /BCK -algebras and we generalize some theorems discussed in BCI -algebras. Moreover, we introduce the notion of “quadratic” Q-algebra, and show that every quadratic Q-algebra (X; ∗, e), e ∈ X, has a product of the form x ∗ y = x − y + e, where x, y ∈ X when X is a field with |X| ≥ 3.
2000 Mathematics Subject Classification. 06F35, 03G25.