Geodesic
Fuzzy ideals and fuzzy congruences on menger algebras with their homomorphism properties
Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 2, pp. 189-206

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It is well known that Menger algebras, sometime called superassociative algebras, play a major role in both mathematical sciences and related areas. The notion of fuzzy sets was initiated by L.A. Zadeh as a general mathematical machinery of classical sets. The present paper establishes a strong interaction between fuzzy sets and Menger algebras. We show that the set of all fuzzy subsets on G together with one (n+1)-ary operations forms a Menger algebra. The concept of several kinds of fuzzy ideals in Menger algebras is introduced and some related properties are investigated. Furthermore, we provide a construction of quotient Menger algebras via fuzzy congruence relations. Finally, homomorphism theorems in terms of fuzzy congruences are studied. Our results can be considered as a generalization in the study of semigroup theory too.
Keywords: Menger algebra, fuzzy ideal, fuzzy congruence relation, quotient Menger algebra 
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Kumduang, Thodsaporn; Chinram, Ronnason. Fuzzy ideals and fuzzy congruences on menger algebras with their homomorphism properties. Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 2, pp. 189-206. http://geodesic.mathdoc.fr/item/DMGAA_2023_43_2_a1/