Fuzzy AT-ideals of AT-algebras

This Book consists of five chapters. We introduce a new notion of algebras called AT-algebras. The notions of AT-algebras, AT-subalgebras, AT-ideals and homomorphism of AT-algebras are introduced. The relation between some abelian groups and AT-algebras are studied and investigated some of its properties . We introduce the notion of fuzzy AT-ideal of AT-algebra, several theorems, properties are stated and proved. the notion of interval-valued fuzzy AT-subalgebras and interval-valued fuzzy AT-ideals on AT-algebras is introduced. We introduced a new notion called cubic AT-ideal of AT-algebras and study several properties of it. we discuss fuzzy ¿-translation, (normalized, maximal) fuzzy S-extension of fuzzy AT-subalgebras in AT-algebra.We discuss fuzzy ¿-translation, fuzzy extension of fuzzy AT-ideals in AT-algebra. We studied and investigated some of its properties.