Home 9 Author: G. Muhiuddin
G. Muhiuddin
Open AccessArticle

Applications of Soft Set Theory to the Subalgebras of CI-Algebras

Annals of Communications in Mathematics 2023

, 6 (2)

, 133-140

DOI: https://doi.org/10.62072/acm.2023.060206

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.
Open AccessArticle

m-polar cubic set theory applied to BCK/BCI-algebras

Annals of Communications in Mathematics 2021

, 4 (3)

, 307-319

DOI: https://doi.org/10.62072/acm.2021.0403010

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.
Open AccessArticle

Prime and irreducible UP-filters of meet-commutative UP-algebras

Annals of Communications in Mathematics 2021

, 4 (2)

, 106-113

DOI: https://doi.org/10.62072/acm.2021.040202

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.
Open AccessArticle

New approach towards A-ideals in ternary semirings

Annals of Communications in Mathematics 2021

, 4 (2)

, 114-125

DOI: https://doi.org/10.62072/acm.2021.040203

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.
Open AccessArticle

Generalizations of implication-based fuzzy subalgebras in BCK/BCI-algebras

Annals of Communications in Mathematics 2021

, 4 (2)

, 180-189

DOI: https://doi.org/10.62072/acm.2021.040211

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.
Open AccessArticle

Hesitant anti-intuitionistic fuzzy soft commutative ideals of BCK-algebras

Annals of Communications in Mathematics 2020

, 3 (2)

, 158-170

DOI: https://doi.org/10.62072/acm.2020.030205

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.
Open AccessArticle

Hesitant intuitionistic fuzzy soft b-ideals of BCK-algebras

Annals of Communications in Mathematics 2020

, 3 (1)

, 26-34

DOI: https://doi.org/10.62072/acm2020030103

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.
Open AccessArticle

Doubt N-ideals theory in BCK-algebras based on N-structures

Annals of Communications in Mathematics 2020

, 3 (1)

, 54-62

DOI: https://doi.org/10.62072/acm.2020.030106

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.
Open AccessArticle

Bipolar fuzzy BCI-implicative ideals of BCI-algebras

Annals of Communications in Mathematics 2020

, 3 (1)

, 88-96

DOI: https://doi.org/10.62072/acm.2020.030109

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.
Open AccessArticle

A generalization of (∈, ∈ ∨q)-fuzzy ideals in ternary semigroups

Annals of Communications in Mathematics 2019

, 2 (2)

, 73-83

DOI: https://doi.org/10.62072/acm.2019.020202

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.
Open AccessArticle

Sup-hesitant fuzzy subalgebras and its translations and extensions

Annals of Communications in Mathematics 2019

, 2 (1)

, 48-56

DOI: https://doi.org/10.62072/acm.2019.020106

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.
Open AccessArticle

Neutrosophic subsemigroups

Annals of Communications in Mathematics 2018

, 1 (1)

, 1-10

DOI: https://doi.org/10.62072/acm.2018.010101

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.
Open AccessArticle

Hybrid structures and applications

Annals of Communications in Mathematics 2018

, 1 (1)

, 11-25

DOI: https://doi.org/10.62072/acm.2018.010102

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.
Open AccessArticle

p-semisimple neutrosophic quadruple BCI-algebras and neutrosophic quadruple p-ideals

Annals of Communications in Mathematics 2018

, 1 (1)

, 26-37

DOI: https://doi.org/10.62072/acm.2018.010103

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.