On Types Algebras

The notion of BCK-algebras was proposed by Y. Iami and K. Iseki in 1966.K. Iseki introduced the notion of a BCI-algebra which is a generalization of BCK-algebra. Since then numerous mathematical papers have been written investigating the algebraic properties of the BCK / BCI-algebras and their relationship with other structures including lattices and Boolean algebras. For the general development of its the ideal theory plays an important role. In the ideal theory of BCI(BCK)-algebras generation of an ideal by a subset in a BCI(BCK)-algebra is an important problem. We devoted to the basic definitions and results concerning several types of algebras and its Fuzzy sets which are required in the succeeding sections. All results here are quoted from existing literature.