In this study, using Yuan and Lee’s definition of fuzzy group based on fuzzy binary operation and Aktas and Cagman definition of fuzzy ring, we give a new kind of definition to (A : B). The concept of fuzzy regular and fuzzy left strongly regular are introduced and we create a new study on their basic properties equivalent to those of ordinary rings. We have shown that if (R, G, H) is strongly regular, then for any a ∈ R, left annihilator of “a” is an ideal.
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