Some Orders in Groupoids and Its Applications to Fuzzy Groupoids
Akbar Rezaei
1
(
Department of Mathematics, Payame Noor University, Tehran, Iran.
)
Choonkil Park
2
(
Department of Mathematics, Hanyang University, Seoul, Korea.
)
Hee Sik Kim
3
(
Department of Mathematics, Hanyang University, Seoul, Korea.
)
کلید واژه: Below, Above, Transitive, Fuzzy, Contractive, Contained, ($\alpha-, \beta-, \gamma_{\alpha}-, \gamma_{\beta}-$)Order-Preserving (reversing).,
چکیده مقاله :
In this paper, we continue the investigation started in [1]. We obtain new results derived from novel concepts developed in analogy with others already established, e.g., the fact that leftoids (X, ∗) for φ are super-transitive if and only if φ(φ(x)) = φ(x) for all x ∈ X. In addition we apply fuzzy subsets in this context and we derive a number of results as consequences.
چکیده انگلیسی :
In this paper, we continue the investigation started in [1]. We obtain new results derived from novel concepts developed in analogy with others already established, e.g., the fact that leftoids (X, ∗) for φ are super-transitive if and only if φ(φ(x)) = φ(x) for all x ∈ X. In addition we apply fuzzy subsets in this context and we derive a number of results as consequences.
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