The UP-Isomorphism Theorems for UP-algebras

In this paper, we construct the fundamental theorem of UP-homomorphisms in UP-algebras. We also give an application of the theorem to the first, second, third and fourth UP-isomorphism theorems in UP-algebras.Comment: 11 page

Introducing fully UP-semigroups

In this paper, we introduce some new classes of algebras related to UP-algebras and semigroups, called a left UP-semigroup, a right UP-semigroup, a fully UP-semigroup, a left-left UP-semigroup, a right-left UP-semigroup, a left-right UP-semigroup, a right-right UP-semigroup, a fully-left UP-semigroup, a fully-right UP-semigroup, a left-fully UP-semigroup, a right-fully UP-semigroup, a fully-fully UP-semigroup, and find their examples.Comment: 8 pages, 1 figur

Fuzzy Translations of a Fuzzy Set in UP-Algebras

In this paper, we apply the concept of fuzzy translations of a fuzzy set to UP-algebras.For any fuzzy set $\mu$ in a UP-algebra,the concepts of fuzzy $\alpha$-translations of $\mu$ of type \textrm{I} and of fuzzy $\beta$-translations of $\mu$ of type \textrm{II} are introduced, their basic properties are investigated and some useful examples are discussed.The concepts of prime fuzzy sets and of weakly prime fuzzy sets in UP-algebras are also studied.Moreover, we discuss the concepts of extensions and of intensions of a fuzzy set in UP-algebras

A generalization of UP-algebras: Weak UP-algebras

Many logical algebras such as BE-, KU- and BCC-algebras have their weak version as generalization. It is known that a CI-algebra is a weak version of a BE-algebra, a JU-algebra is a weak version of a KU-algebra, and a BZ-algebra is a weak version of a BCC-algebra. In this paper, we introduce the concept of weak UP-algebras as a generalization of UP-algebras, and investigate its basic properties. Additionally, some types of ideals in this type of algebras are introduced and analyzed

Atanassov’s intuitionistic fuzzy translations of intuitionistic fuzzy subalgebras in BG-algebras

In this paper, the concepts of intuitionistic fuzzy translation to intuitionistic fuzzy subalgebras in BG-algebras are introduced. The notion of intuitionistic fuzzy extensions and intuitionistic fuzzy multiplications of intuitionistic fuzzy subalgebras are introduced and several related properties are investigated. In this paper, the relationships between intuitionistic fuzzy translations and intuitionistic fuzzy extensions of intuitionistic fuzzy subalgebras are investigated.Publisher's Versio

New types of hesitant fuzzy sets on UP-algebras

The concepts of sup-hesitant fuzzy UP-subalgebras, sup- hesitant 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., sup- hesitant fuzzy UP-filters, sup-hesitant fuzzy UP-ideals, and sup-hesitant fuzzy strongly UP-ideals) and their level subsets

New algebraic structure for Diophantine neutrosophic subbisemirings of bisemirings

The concept of DioNSBSs is introduced in this study. This paper is focused on the following: The introduction is in Section 1. The preliminary definitions and results are found in Section 2. Section 3 introduces the notion of DioNSBS and its several illustrative examples

Tri-Endomorphisms on BCH-Algebras

In this paper, we use the concept of endomorphisms and bi-endomorphisms as a model to create tri-endomorphisms on of BCH-algebras. We introduce the concepts of left tri-endomorphisms, central tri-endomorphisms, right tri-endomorphisms, and complete tri-endomorphisms of BCH-algebras and provide some properties. In addition, we obtain the properties between those tri-endomorphisms and some subsets of BCH-algebras