Using the notion of bipolar-valued fuzzy sets, the concepts of bipolar fuzzy (weak, s-weak, strong) hyper BCK-ideals are introduced, and their relations are discussed in [3]. Further properties are investigated in this article. We show that if Φ = (H ;μΦ , μ N Φ ) is a bipolar fuzzy (weak, strong) hyper BCK-ideal of a hyper BCK-algebra H, then the set I := {x ∈ H | μΦ(x) = μΦ(0), μΦ (x) = μΦ (0...

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A graph G= (V, E) is called a hyper-ring with N nodes (N-HR for short) if V = {0, ..., N-1} and E = {(u,v)| v-u modulo N is a power of 2}. In other words, a hyper-ring with N nodes is a graph in which all of the edges connect nodes that are at distances of powers of 2 from each other. Hyper-rings are a multi-machine organization that is, in a sense, a generalization of the standard hyper-cube a...

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