The notion of bialgebraic structures was discussed by Vasantha Kandasamy [Bialgebraic structures and Smarandache bialgebraic structures. India: American Research Press; 2003]. The main target of this paper is to introduce the notions of a KU-bialgebra, a KP-bialgebra, a PK-bialgebra, and a UP-bialgebra and the notions of a UP-bisubalgebra, a UP-bifilter, a UP-biideal, and a strongly UP-biideal of UP-bialgebras, and prove the generalization of the notions and some results related to a UP-subalgebra, a UP-filter, a UP-ideal, and a strongly UP-ideal of UP-algebras. Furthermore, we introduce the notion of a UP-bihomomorphism and study the image and inverse image of a UP-bisubalgebra, a UP-bifilter, a UP-biideal, and a strongly UP-biideal of UP-bialgebras under a UP-bihomomorphism. Finally, we have the generalization diagram of KU/KP/PK/UP-bialgebras (see Figure 1) and the diagram of special subsets of UP-bialgebras (see Figure 2).

The aim of this paper is to construct the new fundamental theorem of UP-algebras in the meaning of the congruence determined by a UP-homomorphism. We also give an application of the theorem to the first, second, and third UP-isomorphism theorems in UP-algebras.

This paper aims to introduce the notions of anti-hesitant fuzzy UP-subalgebras of UP-algebras, anti-hesitant fuzzy UP-filters, anti-hesitant fuzzy UP-ideals, and anti-hesitant fuzzy strongly UP-ideals, and prove some results. Furthermore, we discuss the relationships between anti-hesitant fuzzy UP-subalgebras (resp., anti-hesitant fuzzy UP-filters, anti-hesitant fuzzy UP-ideals, anti-hesitant fuzzy strongly UP-ideals) and some level subsets of hesitant fuzzy sets on UP-algebras.

The main aim of this paper is to introduce the notion of a partial transformation UP-algebra $P(X)$ induced by a UP-algebra $X$ and prove that the set of all full transformations $T(X)$ is a UP-ideal of $P(X)$.

The concepts of sup-hesitant fuzzy UP-subalgebras, suphesitant fuzzy UP-filters, sup-hesitant fuzzy UP-ideals, and sup-hesitant fuzzy strongly UP-ideals are introduced, proved some results and discussed the generalizations of these concepts. Furthermore, we discuss the relations between sup-hesitant fuzzy UP-subalgebras (resp., suphesitant fuzzy UP-filters, sup-hesitant fuzzy UP-ideals, and sup-hesitant fuzzy strongly UP-ideals) and their level subsets.