This paper aims to extend the concept of cubic sets to neutrosophic sets. The notions of neutrosophic cubic TM-subalgebra, neutrosophic cubic ideal, and neutrosophic cubic T-ideal are introduced, and some related properties are investigated. Some important characteristics of neutrosophic cubic ideal and neutrosophic cubic T-ideal on TM-algebra are discussed. Also, the concept of a level set of a neutrosophic cubic set in TM-algebra is studied.

The concept of bipolar fuzzy ideals in a TM-algebra was introduced and some properties of these ideals are investigated. Also, a few relations between a bipolar fuzzy ideal and T-ideal are discussed. A new bipolar fuzzy set with a homomorphism of TM-algebra is defined. The Cartesian product of bipolar fuzzy T-ideals in Cartesian product TM-algebras is given.

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.

It is known that, the concept of hyper KU-algebras is a generalization of KU-algebras. In this paper, we define cubic (strong, weak,s-weak) hyper KU-ideals of hyper KU-algebras and related properties are investigated.

In this paper, the concept of a neutrosophic KU-algebra is introduced and some related properties are investigated. Also, neutrosophic KU-ideals of a neutrosophic KU-algebra are studied and a few properties are obtained. Furthermore, a few results of neutrosophic KU-ideals of a neutrosophic KU-algebra under homomorphism are discussed

We introduce the notion of interval value fuzzy ideal of TM-algebra as a generalization of a fuzzy ideal of TM-algebra and investigate some basic properties. Interval value fuzzy ideals and T-ideals are defined and several examples are presented. The relation between interval value fuzzy ideal and fuzzy T-ideal is studied. Abstract We introduce the notion of interval value fuzzy ideal of TM-algebra as a generalization of a fuzzy ideal of TM-algebra and investigate some basic properties. Interval value fuzzy ideals and T- ideals are defined and several examples are presented. The relation between interval value fuzzy ideal and fuzzy T-ideal is studied.

The study of homomorphism and Cartesian product is one of the most important mathematical tools that preserve algebraic structures. In this work, a new definition of the concept of a cubic bipolar-ideal under homomorphism in a TM-algebra is introduced. Some important theorems are presented. The notion of Cartesian product for cubic bipolar-ideals and cubic bipolar T-ideals is studied. Also, several properties of the Cartesian product for cubic bipolar-ideals are investigated. Furthermore, the level subsets of the Cartesian product of two cubic bipolar-ideals are defined.

This paper aims to introduce certain new kinds of ideals on pseudo-BG-Algebra (P-BG-A), such as pseudo-closed ideal (P-CI), pseudo-completely closed ideal (P-CCI), and pseudo-n-ideal (P-n-I). Firstly, a (P-n-I) is defined and its pertinent properties are explored. Some important properties have been proven, for example, any pseudo-ideal is a (P-n-I), but the opposite is not generally true, an example was given of the opposite direction. Also, every pseudo-subalgebra of a (P-BG-A) is a pseudo ideal and it is a (P-n-I). Secondly, (P-CI) and a (P-CCI) ideal are defined. After that, we prove that every pseudo-subalgebra of a (P-BG-A) is a (P-CI) and the converse is true. The relationship between (P-BG-A) and pseudo-BH-algebra is demonstrated un