Annals of Communications in Mathematics

AbstractIn this paper, the applicability of soft set theory to subalgebras of CI-algebras is investigated. CI-algebras are utilized in algebraic logic and computer science. Soft set theory is a framework for dealing with ambiguous or imprecise information. We employ soft sets to investigate the intersection and union of subalgebras, among other properties of subalgebras of CI-algebras. We demonstrate that soft set theory is a valuable tool for analyzing subalgebras of CI-algebras and developing new results in this domain. This paper contributes to the comprehension of soft set theory and its applications in CI algebras with the findings presented herein.

AbstractIn this paper, by combinig the notions of m-polar fuzzy structures and interval valued m-polar fuzzy structures, the notion of m-polar cubic structures is introduced and applied on the ideal theory of BCK/BCI-algebras. In this respect, the notions of m-polar cubic subalgebras and m-polar cubic (commutative) ideals are introduced and some essential properties are discussed. Characterizations of m-polar cubic subalgebras and m-polar cubic (commutative) ideals are considered. Moreover, the relations among m-polar cubic subalgebras, m-polar cubic ideals and m-polar cubic commutative ideals are obtained.

AbstractIn this article, we give a number of important properties of meet-commutative UP-algebras. In the class of these UP-algebras, we introduce and analyze the concepts of prime and irreducible UP-filters.

AbstractTo interact somebody with someone various almost ideals (shortly A -ideals), quasi A -ideals, bi quasi A -ideals, tri A -ideals and tri quasi A -ideals in ternary semiring and give some characterizations. We develop the implications ideal =⇒ quasi ideal =⇒ two sided bi quasi ideal =⇒ two sided tri quasi ideal =⇒ two sided tri quasi A -ideal =⇒ two sided bi quasi A -ideal =⇒ bi A -ideal =⇒ quasi A -ideal =⇒ A -ideal and reverse implications do not holds with examples. We show that the union of A -ideals (bi A -ideals, quasi A -ideals, bi quasi A -ideals) is a A -ideal (bi A -ideal, quasi A -ideal, bi quasi A -ideal) in ternary semiring.

AbstractIn [2], Jun discussed implication-based subalgebras in BCK/BCI-algebras. In this article, more general forms than Jun’s results are discussed. We provide an example to show that a fuzzy subalgebra with thresholds 0 and 0.5 is not an implication-based subalgebra under the Łuckasiewicz implication operator, and then conditions for a fuzzy subalgebra with thresholds 0 and 0.5 to be an implication-based subalgebra under the Łuckasiewicz implication operator are provided.

AbstractIn this paper, the notions of hesitant anti-intuitionistic fuzzy soft BCI-commutative ideals of BCI-algebras and hesitant anti-intuitionistic fuzzy soft subcommutative ideals of BCK-algebras are introduced and their related properties are investigate. Relations between a hesitant anti-intuitionistic fuzzy soft ideals and hesitant anti-intuitionistic fuzzy soft BCI-commutative ideals are discussed. Conditions for a hesitant anti-intuitionistic fuzzy soft ideal to be a hesitant anti-intuitionistic fuzzy soft BCIcommutative ideal are provided. Finally, it is proved that a hesitant anti-intuitionistic fuzzy soft p-ideal is a hesitant anti-intuitionistic fuzzy soft sub-commutative ideal in a BCKalgebra.

AbstractIn this paper, we establish the concept of hesitant intuitionistic fuzzy soft ideals and hesitant intuitionistic fuzzy soft b-ideals are introduced and investigated. Also, the power-m, and ρ-multiply are defined in the hesitant intuitionistic fuzzy soft set theory to BCK-algebras. Finally, the newly introduced notions of the complement of a hesitant intuitionistic soft set (ideals and b-ideals) are discussed.

AbstractThe notions of doubt N -subalgebras and doubt N -ideals in BCK-algebras are introduced, and related properties are investigated. Characterizations of a doubt N – subalgebra and a doubt N -ideal are given, and relations between them are discussed.

AbstractThe paper introduces the notions of bipolar fuzzy BCI-implicative ideals and bipolar fuzzy closed BCI-implicative ideals of BCI-algebras. It is proved that any bipolar fuzzy BCI-implicative ideal is a bipolar fuzzy ideal but not the converse. Characterizations of bipolar fuzzy BCI-implicative ideals and bipolar fuzzy closed BCIimplicative ideals are given and more properties are studied.

AbstractThe notion of (α, e βe)-fuzzy left (right, lateral) ideal is introduced, and related properties are investigated. Also, characterizations of an (∈, ∈ ∨ q δ 0 )-fuzzy left (resp., right, lateral) ideal are provided. Moreover, relations between (∈, ∈ ∨ q δ 0 )-fuzzy left (resp., right, lateral) ideal and (q δ 0 , ∈ ∨q δ 0 )-fuzzy left (resp., right, lateral) ideal are established.

AbstractIn BCK/BCI-algebras, the notion of Sup-hesitant fuzzy subalgebra is introduced, and related properties are investigated. Characterizations of a Sup-hesitant fuzzy subalgebra are discussed. Sup-hesitant fuzzy translation and Sup-hesitant fuzzy extension of Sup-hesitant fuzzy subalgebras are introduced, and their relations are investigated.

AbstractIn the present paper, we introduce the notion of (Φ, Ψ)-neutrosophic subsemigroups of a semigroup where Φ, Ψ ∈ {∈, q, ∈ ∨ q}, and related properties are investigated. We consider characterizations of an (∈, ∈)-neutrosophic subsemigroup and an (∈, ∈ ∨ q)-neutrosophic subsemigroup. Conditions for the neutrosophic ∈-subsets, neutrosophic q-subsets and neutrosophic ∈ ∨ q-subsets to be subsemigroups are discussed. Finally, we discuss conditions for a neutrosophic set to be a (q, ∈ ∨ q)-neutrosophic subsemigroup.

AbstractThe notion of hybrid structures is introduced, and several properties are investigated. Applications in BCK/BCI-algebras and linear spaces are discussed. Hybrid subalgebra, hybrid field and hybrid linear space are introduced, and related properties are investigated.

AbstractCharacterizations of neutrosophic quadruple BCI-algebra are considered. Conditions for the neutrosophic quadruple BCI-set to be a p-semisimple BCI-algebra are provided. A condition for a subalgebra to be an ideal in neutrosophic quadruple BCIalgebra is given. Conditions for the set NQ(A, B) to be a neutrosophic quadruple closed ideal and neutrosophic quadruple p-ideal are discussed. Characterizations of neutrosophic quadruple p-ideal are considered.

AbstractAfter BE-algebra was introduced by Kim et al., its generalization was attempted by several scholars. As a follow-up, Borzooei et al., Rezaei et al. and Sayyad et al. introduced pseudo BE-algebra, eBE-algebra and pseudo eBE-algebra, respectively. The aim of this article is to consider more extended version of pseudo eBE-algebra. The concepts of generalized pseudo eBE-algebra, (generalized) pseudo sub-eBE-algebra, eBEsubalgebra, eBE-filter, right (left) f-section and eBE-upper set are introduced and related properties, interrelationships and characterizations are studied.

AbstractA semigroup is an algebraic structure that consists of a set and a binary operation that is associative, meaning that the order in which the operations are performed does not affect the outcome. For example, addition and multiplication are associative operations. The term “semigroup” was first used in its modern sense by Harold Hilton in his book on finite groups in 1908 [6]. Semigroups have since then been studied extensively in mathematics, and they have numerous applications in different fields, such as computer science, physics, and economics. Nearenness semigroup is a generalization of semigroups. Near set theory, which is a generalization of rough set theory, is based on the determination of universal sets according to the available information about the objects. Nearenness semigroups extend the concept of nearness from set theory to semigroups. ˙Inan and Öztürk applied the notion of near sets defined by J. F. Peters to the semigroups [10]. Our objective in this paper is to establish the definition of ordered semigroups on weak near approximation spaces. In addition, we investigated certain characteristics of these ordered nearness semigroups.