Single-Valued Neutro Hyper BCK-Subalgebras

Hamidi, Mohammad; Smarandache, Florentín

doi:10.1155/2021/6656739

Cited by 3 publications

(2 citation statements)

References 13 publications

(11 reference statements)

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“…Single-valued neutrosophic set has been developing rapidly due to its wide range of theoretical elegance and application areas. The reader may refer to the following articles [7,8,16,17,19,20] as references. In 1999, Molodtsov [14] studied another mathematical theory called soft set theory by giving parameterized approach to uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Single-valued Neutrosophic Soft Sets in Hyper UP-Algebra

Cano

Petalcorin²

2023

Eur. J. Pure Appl. Math.

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In this paper, the notions of SVN hyper UP-algebra and SVNS hyper UP-algebra are introduced, and some of their structural properties are investigated. Moreover, the Cartesian product of SVNS hyper UP-algebra is discussed and proved to be a SVNS hyper UP- algebra. Finally, the homomorphic image and preimage of SVNS hyper UP-algebra under SVNS functions are studied and showed also to be SVNS hyper UP-algebra.

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Section: Introductionmentioning

confidence: 99%

Single-valued Neutrosophic Soft Sets in Hyper UP-Algebra

Cano

Petalcorin²

2023

Eur. J. Pure Appl. Math.

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“…Zaronzy et al [21] introduced the concept of a bipolar query, meant as a database query that involves both negative and positive conditions. Hamidi et al [22,23] extended BCK-ideal based on single-valued neutrosophic hyper BCK-ideals. The motivation and contributions of this study are as follows (Table 1):…”

Section: Introductionmentioning

confidence: 99%

Bipolar Intuitionistic Fuzzy Soft Ideals of BCK/BCI-Algebras and Its Applications in Decision-Making

Balamurugan,

Alessa,

Loganathan

et al. 2023

Mathematics

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In this paper, we merge the concepts of soft set theory and a bipolar intuitionistic fuzzy set. A bipolar intuitionistic fuzzy soft ideal in a BCK-algebra is defined as a soft set over the set of elements in the BCK-algebra, with each element associated with an intuitionistic fuzzy set. This relationship captures degrees of uncertainty, hesitancy, and non-membership degrees within the context of BCK-algebras. We investigate basic operations on bipolar intuitionistic fuzzy soft ideals such as union, intersection, AND, and OR. The intersection, union, AND, and OR of two bipolar intuitionistic fuzzy soft ideals is a bipolar intuitionistic fuzzy soft ideal. We also demonstrate how to use a bipolar intuitionistic fuzzy soft set to solve a problem involving decision making. Finally, we provide a general approach for handling decision-making problems using a bipolar intuitionistic fuzzy soft set.

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Extended BCK-Ideal Based on Single-Valued Neutrosophic Hyper BCK-Ideals

Hamidi

2023

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This paper introduces the concept of single-valued neutrosophic hyper \(BCK\)-subalgebras as a generalization and alternative of hyper \(BCK\)-algebras and on any given nonempty set constructs at least one single-valued neutrosophic hyper \(BCK\)-subalgebra and one a single-valued neutrosophic hyper \(BCK\)-ideal. In this study level subsets play the main role in the connection between single-valued neutrosophic hyper \(BCK\)-subalgebras and hyper \(BCK\)-subalgebras and the connection between single-valued neutrosophic hyper \(BCK\)-ideals and hyper \(BCK\)-ideals. The congruence and (strongly) regular equivalence relations are the important tools for connecting hyperstructures and structures, so the major contribution of this study is to apply and introduce a (strongly) regular relation on hyper \(BCK\)-algebras and to investigate their categorical properties (quasi commutative diagram) via single-valued neutrosophic hyper \(BCK\)-ideals. Indeed, by using the single-valued neutrosophic hyper \(BCK\)-ideals, we define a congruence relation on (weak commutative) hyper \(BCK\)-algebras that under some conditions is strongly regular and the quotient of any (single-valued neutrosophic)hyper \(BCK\)-(sub)algebra via this relation is a (single-valued neutrosophic)(hyper \(BCK\)-subalgebra) \(BCK\)-(sub)algebra.

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Single-Valued Neutro Hyper BCK-Subalgebras

Cited by 3 publications

References 13 publications

Single-valued Neutrosophic Soft Sets in Hyper UP-Algebra

Single-valued Neutrosophic Soft Sets in Hyper UP-Algebra

Bipolar Intuitionistic Fuzzy Soft Ideals of BCK/BCI-Algebras and Its Applications in Decision-Making

Extended BCK-Ideal Based on Single-Valued Neutrosophic Hyper BCK-Ideals

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