In This paper, we introduce the associated graphs of commutative KU-algebra. Firstly, we define the KU-graph which is determined by all the elements of commutative KU-algebra as vertices. Secondly, the graph of equivalence classes of commutative KU-algebra is studied and several examples are presented. Also, by using the definition of graph folding, we prove that the graph of equivalence classes and the graph folding of commutative KU-algebra are the same, where the graph is complete bipartite graph.

In thisˑ paperˑ, we apply the notion ofˑ intuitionisticˑ fuzzyˑ n-fold KU-ideal of KU-algebra. Some types of ideals such as intuitionistic fuzzy KU-ideal, intuitionisticˑ fuzzy closed idealˑ and intuitionistic fuzzy n-fold KU-ideal are studied. Also, the relations between intuitionistic fuzzy n-fold KU-ideal and intuitionistic fuzzy KU-ideal are discussed. Furthermore, aˑ fewˑ results of intuitionisticˑ fuzzyˑ n-ˑfold KU-ideals of a KU-algebra underˑ homomorphismˑ are discussed.

An intuitionistic fuzzy set was exhibited by Atanassov in 1986 as a generalization of the fuzzy set. So, we introduce cubic intuitionistic structures on a KU-semigroup as a generalization of the fuzzy set of a KU-semigroup. A cubic intuitionistic k-ideal and some related properties are introduced. Also, a few characterizations of a cubic intuitionistic k-ideal are discussed and new cubic intuitionistic fuzzy sets in a KU-semigroup are defined.

In this work, we apply the notion of a filter of a KU-Algebra and investigate several properties. The paper defined some filters such as strong filter, n-fold filter and P-filter and discussed a few theorems and examples.