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المقاله
1 - Fuzzy Subgroups and Digraphs Induced by Fuzzy SubgroupsTransactions on Fuzzy Sets and Systems , العدد 1 , السنة 1 , بهار-تابستان 2022Given a fuzzy subgroup $\mu$ of a group $G$, $x\rhd_uy$ if and only if $\mu(xy) < \mu(yx)$ defines a directed relation with an associated digraph $(G, \rhd_u)$. We consider $(\mu, \nu)$-homomorphisms $\varphi: (G, \mu)\to (H, \nu)$ where $\mu$ and $\nu$ ar أکثرGiven a fuzzy subgroup $\mu$ of a group $G$, $x\rhd_uy$ if and only if $\mu(xy) < \mu(yx)$ defines a directed relation with an associated digraph $(G, \rhd_u)$. We consider $(\mu, \nu)$-homomorphisms $\varphi: (G, \mu)\to (H, \nu)$ where $\mu$ and $\nu$ are fuzzy subgroups of $G$ and $H$ respectively and the preservation of properties of the digraphs $(G, \rhd_u)$ several of which are also noted here, e.g., $(G, \rhd_u)$ is an anti-chain if and only if $\mu$ is a fuzzy normal subgroup of the group $G$. تفاصيل المقالة -
المقاله
2 - Some Orders in Groupoids and Its Applications to Fuzzy GroupoidsTransactions on Fuzzy Sets and Systems , العدد 7 , السنة 4 , بهار-تابستان 2025In 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 ∈ أکثرIn 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. تفاصيل المقالة