Abstract
Some new notions of fuzzy algebras like fuzzy $$\rho $$ -subalgebra, fuzzy $$\rho $$ -ideal, and fuzzy $${\overline{\rho }}$$ -ideal are introduced in this work. Moreover, the relationships between our new notions and other types of fuzzy algebras like fuzzy d-subalgebra, fuzzy d-ideal, fuzzy BCK-subalgebra, and fuzzy BCK-ideal are investigated. Also, some basic characterizations of fuzzy $$\rho $$ -ideal with their applications on images, Cartesian product, upper level, characteristic function, and strongest fuzzy relation are studied and discussed in this paper. Furthermore, several examples are presented to expound our notions in this work.
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