Regularity of interval fuzzy matrices

Myšková, Helena; Plávka, Ján

doi:10.1016/j.fss.2023.01.013

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2024

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“…Kumduang and Chinram [24] investigated fuzzy ideals and fuzzy congruences in Menger algebras. Furthermore, various scholars [25][26][27] have examined alternative approaches to analyzing distinct algebraic structures. Since associative algebra is a very important class of algebraic structures, its theories can be applied to group, ring, and semiring structures.…”

Section: Introductionmentioning

confidence: 99%

Ideals and Homomorphism Theorems of Fuzzy Associative Algebras

Yang,

Zhou

2024

Mathematics

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Based on the definitions of fuzzy associative algebras and fuzzy ideals, it is proven that the intersections of fuzzy subalgebras are fuzzy subalgebras, and the intersections of fuzzy ideals are fuzzy ideals. Moreover, we prove that the kernels of fuzzy homomorphisms are fuzzy ideals. Using fuzzy ideals, the quotient structures of fuzzy associative algebras are constructed, their corresponding properties are discussed, and their homomorphism theorems are proven.

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