Explanipedia

Stone Paradistributive Latticoids Open

Ravikumar Bandaru, Ramesh Sirisetti, Satyanarayana Rao Kola, N. Rafi, Hashem Bordbar , et al. · 2025

We introduce the concept of Stone paradistributive latticoids (Stone PDLs) as a natural generalization of Stone lattices to the broader setting of paradistributive latticoids endowed with parapseudo-complementation. We provide multiple equ…

Lukasiewicz Fuzzy Set Theory Applied to SBE-Algebras Open

Tahsin Öner, Hashem Bordbar, N. Rajesh, Akbar Rezaei · 2025

In this paper, we utilize the Lukasiewicz t-norm to construct a novel class of fuzzy sets, termed ζ-Lukasiewicz fuzzy sets, derived from a given fuzzy framework. These sets are then applied to the structure of Sheffer stroke BE-algebras (S…

On ps-Supplement Submodules Open

İrfan Soydan, Ergül Türkmen, Hashem Bordbar · 2025

In this work, we introduce ps-supplement submodules as a kind of supplements. Specifically, a submodule V of a module M is referred to as a ps-supplement if there exists another submodule U⊆M such that M=U+V and the intersection U∩V is pro…

On Subprojectivity of Goldie Torsion Modules Open

Hashem Bordbar, Yılmaz Durğun, Yara Şihkayad, Ergül Türkmen · 2025

Recently, the concept of subprojectivity domains for modules has been introduced as a means of quantifying the level of projectivity exhibited by a module. In this research article, we focus on the subprojectivity domain of Goldie torsion …

Soft GE-algebras Open

Hashem Bordbar, Ravikumar Bandaru, Young Bae Jun · 2025

In this paper, we introduce the concept of soft GE-algebras within the framework of GE-algebra theory, extending existing approaches by incorporating principles of soft set theory. We investigate the structural properties of soft GE-algebr…

An Investigation into Bipolar Fuzzy Hoop Algebras and Their Applications Open

Tahsin Öner, Rajesh Neelamegarajan, Ravikumar Bandaru, Hashem Bordbar · 2025

This paper introduces bipolar fuzzy sub-hoops and bipolar fuzzy filters within hoop algebras, extending fuzzy logic to incorporate both positive and negative membership degrees. We define these structures, explore their algebraic propertie…

SBE-Algebras via Intuitionistic Fuzzy Structures Open

Tahsin Öner, Hashem Bordbar, Neelamegarajan Rajesh, Akbar Rezaei · 2024

The study introduces the concept of intuitionistic fuzzy SBE-subalgebras, ideals, and filters, along with level sets of intuitionistic fuzzy sets within the framework of Sheffer stroke BE-algebras. These concepts are shown to be crucial fo…

Ordered algebraic structure in a linear code Open

Hashem Bordbar · 2024

Computational Algebra, Coding Theory, and Cryptography: Theory and Applications Open

Hashem Bordbar · 2024

The primary aim of this Special Issue is to explore innovative encoding and decoding procedures that leverage various algebraic structures to enhance error-control coding techniques [...]

A Characterization of Normal Injective and Normal Projective Hypermodules Open

Ergül Türkmen, Burcu Nişancı Türkmen, Hashem Bordbar · 2024

This study is motivated by the recently published papers on normal injective and normal projective hypermodules. We provide a new characterization of the normal injective and normal projective hypermodules by using the splitting of the sho…

Sheffer Stroke Hilbert Algebras Stabilizing by Ideals Open

Tuğçe Katıcan, Hashem Bordbar · 2024

This manuscript aims to provide a new characterization of Sheffer stroke Hilbert algebras due to their ideals and proposes stabilizers. In the setup of the main results, we construct particular subsets of Sheffer stroke Hilbert algebras an…

A Hyperstructural Approach to Semisimplicity Open

Ergül Türkmen, Burcu Nişancı Türkmen, Hashem Bordbar · 2024

In this paper, we provide the basic properties of (semi)simple hypermodules. We show that if a hypermodule M is simple, then (End(M),·) is a group, where End(M) is the set of all normal endomorphisms of M. We prove that every simple hyperm…

Łukasiewicz Anti Fuzzy Subalgebras of BCK/BCI-Algebras Open

Jeong Gi Kang, Hashem Bordbar · 2024

The subalgebra of BCK/BCI-algebra using Łukasiewicz anti fuzzy set introduced by Jun is studied in this article. The concept of Łukasiewicz anti fuzzy subalgebra of a BCK/BCI-algebra is introduced, and several properties are investigated. …

Torsion Elements and Torsionable Hypermodules Open

Hashem Bordbar · 2023

This article is motivated by the recently published studies on divisible hypermodules and falls in the area of hypercompositional algebra. In particular, it focuses on the torsion elements in Krasner hypermodules. First, we define the conc…

Preface to the Special Issue “Algebraic Structures and Graph Theory” Open

Irina Cristea, Hashem Bordbar · 2023

Connections between algebraic structure theory and graph theory have been established in order to solve open problems in one theory with the help of the tools existing in the other, emphasizing the remarkable properties of one theory with …

Positive implicative cubic intuitionistic ideals in BCK-algebras Open

Hashem Bordbar, Young Bae Jun · 2023

Conditions for a cubic intuitionistic set to be a cubic intuitionistic ideal are provided. Positive implicative cubic intuitionistic ideal in BCK-algebras is introduced, and related properties are investigated. Characterizations of positiv…

Semihypergroup-Based Graph for Modeling International Spread of COVID-n in Social Systems Open

Narjes Firouzkouhi, R. Ameri, Abbas Amini, Hashem Bordbar · 2022

Graph theoretic techniques have been widely applied to model many types of links in social systems. Also, algebraic hypercompositional structure theory has demonstrated its systematic application in some problems. Influenced by these mathe…

Supplements Related to Normal π-Projective Hypermodules Open

Burcu Nişancı Türkmen, Hashem Bordbar, Irina Cristea · 2022

In this study, the role of supplements in Krasner hypermodules is examined and related to normal π-projectivity. We prove that the class of supplemented Krasner hypermodules is closed under finite sums and under quotients. Moreover, we giv…

The Structure of the Block Code Generated by a BL-Algebra Open

Hashem Bordbar · 2022

Inspired by the concept of BL-algebra as an important part of the ordered algebra, in this paper we investigate the binary block code generated by an arbitrary BL-algebra and study related properties. For this goal, we initiate the study o…

Positive implicative ideals of BCK-algebras based on neutrosophic sets and falling shadows Open

Hashem Bordbar, Xiao Long Xin, R. A. Borzooei, Young Bae Jun · 2022

Neutrosophy is introduced by F. Smarandache in 1980 which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophy considers a proposition, theory, event, concept, …

Divisible hypermodules Open

Hashem Bordbar, Irina Cristea · 2022

The article is motivated by the recently published studies on injective and projective hypermodules. We present here a new characterization of the normal injective hypermodules. First we define the concept of zero-divisors over a hypermodu…

Regular local hyperrings and hyperdomains Open

Hashem Bordbar, Sanja Jančić-Rašović, Irina Cristea · 2022

This paper falls in the area of hypercompositional algebra. In particular it focuses on the class of Krasner hyperrings and it studies the regular local hyperrings. These are Krasner hyperrings $ R $ with a unique maximal hyperideal $ M $ …

N-subalgebras of BCK=BCI-Algebras which are Induced from Hyperfuzzy Structures Open

Hashem Bordbar, Maryam Bordbar, R. A. Borzooei, Y. B. Jun · 2021

Ghosh and Samanta introduced the concept of hyperfuzzy sets as a generalization of fuzzy sets and interval-valued fuzzy sets, and applied it to group theory.The aim of this manuscript is to study N -structures in BCK/BCI-algebras induced f…

About the Normal Projectivity and Injectivity of Krasner Hypermodules Open

Hashem Bordbar, Irina Cristea · 2021

Inspired by the concepts of projective and injective modules in classical algebraic structure theory, in this paper we initiate the study of the chains of hypermodules over a Krasner hyperring R, endowing first the set HomRn(M,N) of all no…

Soft subalgebras and ideals of BCK|BCI-algebras based on Ɲ-structures Open

Hashem Bordbar, R. A. Borzooei, Arsham Borumand Saeid, Young Bae Jun · 2021

The notions of Ɲ-ideal of types (∈,∈) and (∈,∈Vq), soft Ɲ_∈-set, soft Ɲ_q-set, soft Ɲ_∈vq-set, soft Ɲ-subalgebra and soft Ɲ-ideal in BCK|BCI-algebra are introduced, and several properties are investigated. Cha…

Internal and External Cubic Subalgebras of BCK/BCI-Algebras Open

Hashem Bordbar, M. M. Zahedi, Young Bae Jun · 2021

A characterization of cubic subalgebra is established. The notion of internal and external cubic subalgebra in BCK/BCI-algebra and several properties are investigated. The R-union, R-intersection, P-union, and P-intersection of internal an…

Implicative falling neutrosophic ideals of BCK-algebras Open

Xiao Long Xin, Hashem Bordbar, Florentín Smarandache, R. A. Borzooei, Young Bae Jun · 2021

The notions of an implicative (∈, ∈)-neutrosophic ideal and an implicative falling neutrosophic ideal are introduced, and several properties are investigated. Characterizations of an implicative (∈, ∈)-neutrosophic ideal are considered, an…

Regular Parameter Elements and Regular Local Hyperrings Open

Hashem Bordbar, Irina Cristea · 2021

Inspired by the concept of regular local rings in classical algebra, in this article we initiate the study of the regular parameter elements in a commutative local Noetherian hyperring. These elements provide a deep connection between the …

Interior BCK/BCI-Algebras Open

Sun Shin Ahn, Hashem Bordbar, Young Bae Jun · 2021

A General Model of Neutrosophic Ideals in BCK/BCI-algebras Based on Neutrosophic Points Open

Hashem Bordbar, R. A. Borzooei, Florentín Smarandache, Young Bae Jun · 2020

More general form of (∈, ∈ ∨q)-neutrosophic ideal is introduced, and their properties are investigated. Relations between (∈, ∈)-neutrosophic ideal and (∈, ∈ ∨q(kT ,kI ,kF ))-neutrosophic ideal are discussed. Characterizations of (∈,…

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