‎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. )

Submited date : 2024-05-13 Accepted date : 2024-07-25

Keywords: Below‎, ‎Above‎, ‎Transitive‎, ‎Fuzzy‎, ‎Contractive‎, ‎Contained‎, ‎($\alpha-‎, ‎\beta-‎, ‎\gamma_{\alpha}-‎, ‎\gamma_{\beta}-$)Order-Preserving (reversing)‎.,

Abstract :

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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