Let G be a fuzzy graph. A subset D of V is said to be Fuzzy dominating set if every vertex u ∈ V (G) there exists a vertex v ∈ V −D such that uv ∈ E(G) and μ(uv) 6 σ(u) ∧ σ(v). The minimum Cardinality of fuzzy dominating set is denoted by γf . A graph G is said to be fuzzy excellent if every vertex of G belongs to γf -sets of G. In this paper, we give a construction to imbedded non-excellent fu...

Discussion on implementation of the Excellent Care for all Act, 2010 (ECFA Act), Bill 46, has focused on the hospital sector in Ontario, but it also has relevance outside the hospital setting. As primary healthcare, long-term care and home care all receive public funding, these sectors should be expected to be compliant with Bill 46. But does the act also govern government-funded (i.e., by othe...

In this paper, we present Shelah’s theory of excellence concluding with his categoricity theorem for the class of atomic models of a countable first order theory, under the assumption that there exists a large full model. This allows us to do the entire work within ZFC and without any assumption on the number of models of size א1, in contrast to Shelah’s original treatment.