We introduce the notion of cubic KU-ideals of KU-algebras and several results are presented in this regard. The image, preimage, and cartesian product of cubic KU-ideals of KU-algebras are defined.

In this article, we introduce the concept of graphs associated with commutative UP-algebra, which we say is a UP-graph whose vertices are the elements of commutative UP-algebra and whose edges are the association of two vertices, that is two elements from commutative UP-algebra. We also define a graph of equivalence classes of a commutative UP-algebra and prove some related results based on the algebraic properties of the graph. We show that two graphs are the same and complete bipartite if they are formed by equivalence classes of UP-algebra and the graph folding of commutative UP-algebra. An algorithm for checking whether a given set is a UP-algebra or not has also been given.

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In this paper we have introduced the concept of pseudo-valuations on JU-algebras and have investigated the relationship between pseudo-valuations and ideals of JU-algebras. Conditions for a real-valued function to be a pseudo-valuation on JU-algebras are given and results based on them have been shown. We have also defined and studied pseudo-metric on JU-algebras and have proved that ϑ being a valuation on a JU-algebras A, the operation in A is uniformly continuous.

The purpose of this paper is to introduce and discuss the concept of T-rough ternary subsemigroups, T-rough ideals, T-rough bi-ideals and T-rough interior ideals in ternary semigroups.