This study investigated the cubic intuitionistic fuzzy set of TM-algebra as a generalization of the cubic set. First, a cubic intuitionistic ideal and a cubic intuitionistic T-ideal are defined, followed by a discussion of their properties. Furthermore, the level set of a cubic intuitionistic TM-algebra is defined, and the relationship between a cubic intuitionistic level set and the cubic intuitionistic T-ideal is established. A novel definition of a cubic intuitionistic set under homomorphism is proposed, and several significant results are demonstrated.

This paper refers to studying some types of ideals, specifically cubic bipolar ideals and cubic bipolar T-ideals of TM algebra. It also introduces a cubic bipolar sub-TM-algebra and several important properties of these concepts. The relationships between these ideals and characterizations of cubic bipolar T-ideals are investigated.

We have studied some types of ideals in a KU-semigroup by using the concept of a bipolar fuzzy set. Bipolar fuzzy S-ideals and bipolar fuzzy k-ideals are introduced, and some properties are investigated. Also, some relations between a bipolar fuzzy k-ideal and k-ideal are discussed. Moreover, a bipolar fuzzy k-ideal under homomorphism and the product of two bipolar fuzzy k-ideals are studied.

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.

The notion of interval value fuzzy k-ideal of KU-semigroup was studied as a generalization of afuzzy k-ideal of KU-semigroup. Some results of this idea under homomorphism are discussed. Also, we presented some properties about the image (pre-image) for interval~ valued fuzzy~k-ideals of a KU-semigroup. Finally, the~ product of~ interval valued fuzzyk-ideals is established.

In this paper, we apply the notion of a bipolar fuzzy n-fold KU-ideal of KU- algebras. We introduce the concept of a bipolar fuzzy n-fold KU-ideal and investigate several properties. Also, we give relations between a bipolar fuzzy n- fold KU-ideal and n-fold KU-ideal. The image and the pre-image of bipolar fuzzy n-fold KU-ideals in KU-algebras are defined and how the image and the pre- image of bipolar fuzzy n-fold KU-ideals in KU-algebras become bipolar fuzzy n- fold KU-ideals are studied. Moreover, the product of bipolar fuzzy n-fold KU- ideals in Cartesian product KU-algebras is given.

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.

In this paper, we introduce the concepts of positive implicative [resp. implicative and commutative] Γ-KU-algebras, and obtain their some properties (including characterizations) respectively and some relationships among them. Next, we propose the notions of positive implicative [resp. implicative and commutative] Γ-ideals of a Γ-KU-algebra, and deal with their some properties (including characterizations) respectively and some relationships among them. Finally, we define a topological Γ-KU-algebra and discuss its various topological structures.