scholarly journals A Note on Single Valued Neutrosophic Sets in Ordered Groupoids

2020 ◽  
pp. 73-83
Author(s):  
admin admin ◽  
◽  
◽  
◽  
B. Davvaz ◽  
...  
Keyword(s):  
Algebraic Structures ◽  
Neutrosophic Sets ◽  
Ordered Groups ◽  
First Time

The aim of this paper is to combine the notions of ordered algebraic structures and neutrosophy. In this regard, we define for the first time single valued neutrosophic sets in ordered groupoids. More precisely, we study single valued neutrosophic subgroupoids of ordered groupoids, single valued neutrosophic ideals of ordered groupoids, and single valued neutrosophic filters of ordered groupoids. Finally, we present some remarks on single valued neutrosophic subgroups (ideals) of ordered groups.

On single valued neutrosophic sets and neutrosophic א-structures: Applications on algebraic structures (hyperstructures)

2020 ◽  
pp. 108-117
Author(s):  
Madeleine Al Al-Tahan ◽  
◽  
◽  
Bijan Davvaz
Keyword(s):  
Algebraic Structure ◽  
Algebraic Structures ◽  
Neutrosophic Sets

In this paper, we find a relationship between SVNS and neutrosophic N-structures and study it. Moreover, we apply our results to algebraic structures (hyperstructures) and prove that the results on neutrosophic N-substructure (subhyperstructure) of a given algebraic structure (hyperstructure) can be deduced from single valued neutrosophic algebraic structure (hyperstructure) and vice versa.

A class of constacyclic codes from group algebras

Filomat ◽  
2017 ◽  
Vol 31 (10) ◽  
pp. 2917-2923
Author(s):  
Mehmet Koroglu ◽  
Irfan Siap
Keyword(s):  
Cyclic Codes ◽  
Group Algebras ◽  
Constacyclic Codes ◽  
Algebraic Structures ◽  
Engineering Applications ◽  
Negacyclic Codes ◽  
Zero Divisors ◽  
First Time

Constacyclic codes are preferred in engineering applications due to their efficient encoding process via shift registers. The class of constacyclic codes contains cyclic and negacyclic codes. The relation and presentation of cyclic codes as group algebras has been considered. Here for the first time, we establish a relation between constacyclic codes and group algebras and study their algebraic structures. Further, we give a method for constructing constacyclic codes by using zero-divisors in group algebras. Some good parameters for constacyclic codes which are derived from the proposed construction are also listed.

Refined Neutrosophic Rings I

2020 ◽  
pp. 77-81
Author(s):  
E.O. Adeleke ◽  
◽  
◽  
◽  
A.A.A. Agboola ◽  
...  
Keyword(s):  
Neutrosophic Set ◽  
Algebraic Structures ◽  
Neutrosophic Logic ◽  
First Time

The notion of neutrosophic ring R(I) generated by the ring R and the indeterminacy component I was introduced for the first time in the literature by Vasantha Kandasamy and Smarandache in.12 Since then, fur-ther studies have been carried out on neutrosophic ring, neutrosophic nearring and neutrosophic hyperring see.1, 3, 4, 6–8 Recently, Smarandache10 introduced the notion of refined neutrosophic logic and neutrosophic set with the splitting of the neutrosophic components T, I, F into the form T1, T2, . . . , Tp; I1, I2, . . . , Ir; F1, F2, . . . , Fs where Ti, Ii, Fi can be made to represent different logical notions and concepts. In,11 Smarandache introduced refined neutrosophic numbers in the form (a, b1I1, b2I2, . . . , bnIn) where a, b1, b2, . . . , bn ∈ R or C. The concept of refined neutrosophic algebraic structures was introduced by Agboola in5 and in particular, refined neutrosophic groups and their substructures were studied. The present paper is devoted to the study of refined neutrosophic rings and their substructures. It is shown that every refined neutrosophic ring is a ring. For the purposes of this paper, it will be assumed that I splits into two indeterminacies I1 [contradiction (true (T) and false (F))] and I2 [ignorance (true (T) or false (F))]. It then follows logically that:

A study of refined neutrosophic complex numbers and their algebriac properties

2021 ◽  
Author(s):  
Malath F. Alaswad ◽  
Keyword(s):  
Direct Application ◽  
Complex Numbers ◽  
Polar Form ◽  
Neutrosophic Sets ◽  
Algebraic Operations ◽  
First Time

This paper is dedicated to defining for the first time the concept of complex refined neutrosophic numbers as a direct application of refined neutrosophic sets and as a new generalization of neutrosophic complex numbers. Also, it presents some of their elementary properties such as conjugates, absolute values, invertibility, and algebraic operations. The importance of the definitions in this article lies in the use of them by defining the polar form of the refined neutrosophic complex numbers.

scholarly journals A New Approach for Optimization of Real Life Transportation Problem in Neutrosophic Environment

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
A. Thamaraiselvi ◽  
R. Santhi
Keyword(s):  
Fuzzy Sets ◽  
Real World ◽  
Transportation Problem ◽  
Real Life ◽  
Intuitionistic Fuzzy Sets ◽  
Mathematical Representation ◽  
Neutrosophic Sets ◽  
New Approach ◽  
Real World Problem ◽  
First Time

Neutrosophic sets have been introduced as a generalization of crisp sets, fuzzy sets, and intuitionistic fuzzy sets to represent uncertain, inconsistent, and incomplete information about a real world problem. For the first time, this paper attempts to introduce the mathematical representation of a transportation problem in neutrosophic environment. The necessity of the model is discussed. A new method for solving transportation problem with indeterminate and inconsistent information is proposed briefly. A real life example is given to illustrate the efficiency of the proposed method in neutrosophic approach.

scholarly journals Neutrosophic Multigroups and Applications

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 95 ◽  
Author(s):  
Vakkas Uluçay ◽  
Memet Şahin
Keyword(s):  
Group Theory ◽  
Set Theory ◽  
Algebraic Structure ◽  
Group Structure ◽  
Algebraic Structures ◽  
Neutrosophic Sets ◽  
Basic Properties

In recent years, fuzzy multisets and neutrosophic sets have become a subject of great interest for researchers and have been widely applied to algebraic structures include groups, rings, fields and lattices. Neutrosophic multiset is a generalization of multisets and neutrosophic sets. In this paper, we proposed a algebraic structure on neutrosophic multisets is called neutrosophic multigroups which allow the truth-membership, indeterminacy-membership and falsity-membership sequence have a set of real values between zero and one. This new notation of group as a bridge among neutrosophic multiset theory, set theory and group theory and also shows the effect of neutrosophic multisets on a group structure. We finally derive the basic properties of neutrosophic multigroups and give its applications to group theory.

scholarly journals A Note on Neutrosophic Submodule of an R-module M

2020 ◽  
pp. 118-127
Author(s):  
Binu R ◽  
Keyword(s):  
Set Theory ◽  
Neutrosophic Set ◽  
Sufficient Condition ◽  
Algebraic Structures ◽  
Necessary And Sufficient Condition ◽  
Neutrosophic Sets ◽  
Algebraic Operations ◽  
Necessary And Sufficient

The paper focuses on the applications of neutrosophic set theory in the domain of classical algebraic structures, especially R-module. This study discusses some algebraic operations of neutrosophic sets of an R-moduleM, induced by the operations in M and demonstrates certain properties of the neutrosophic submodules of an R-module. The ideas of R module’s non-empty arbitrary family of neutrosophic submodules are characterized, and related outcomes are proved. The last section of this paper also derives a necessary and sufficient condition for a neutrosophic set of an R-module M.

scholarly journals Optimal Solution of Neutrosophic Linear Fractional Programming Problems With Mixed Constraints

2022 ◽  
Author(s):  
SAPAN DAS ◽  
S A Edalatpanah
Keyword(s):  
Fractional Programming ◽  
Numerical Models ◽  
Optimal Solution ◽  
Triangular Fuzzy Number ◽  
Contextual Analysis ◽  
The Novel ◽  
Linear Fractional Programming ◽  
Neutrosophic Sets ◽  
First Time ◽  
Better Than

Abstract In this paper, Linear Fractional Programming (LFP) problems have been extended to neutrosophic sets (NSs) and the operations and functionality of these laws are studied. Moreover, the new algorithm is based on aggregation ranking function and arithmetic operations of triangular neutrosophic sets (TNSs). Furthermore, for the first time, in this paper, we take up a problem where the constraints are both equality and inequality neutrosophic triangular fuzzy number. Lead from genuine issue, a few numerical models are considered to survey the legitimacy, profitability and materialness of our technique. At last, some numerical trials alongside one contextual analysis are given to show the novel techniques are better than the current strategies.

scholarly journals Neutrosophic Components Semigroups and Multiset Neutrosophic Components Semigroups

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 818
Author(s):  
Vasantha W. B. ◽  
Ilanthenral Kandasamy ◽  
Florentin Smarandache
Keyword(s):  
Commutative Ring ◽  
Infinite Number ◽  
Unit Element ◽  
Product Form ◽  
Algebraic Structures ◽  
Zero Divisors ◽  
Free Semigroups ◽  
First Time ◽  
Torsion Free ◽  
Usual Product

Neutrosophic components (NC) under addition and product form different algebraic structures over different intervals. In this paper authors for the first time define the usual product and sum operations on NC. Here four different NC are defined using the four different intervals: (0, 1), [0, 1), (0, 1] and [0, 1]. In the neutrosophic components we assume the truth value or the false value or the indeterminate value to be from the intervals (0, 1) or [0, 1) or (0, 1] or [0, 1]. All the operations defined on these neutrosophic components on the four intervals are symmetric. In all the four cases the NC collection happens to be a semigroup under product. All of them are torsion free semigroups or weakly torsion free semigroups. The NC defined on the interval [0, 1) happens to be a group under addition modulo 1. Further it is proved the NC defined on the interval [0, 1) is an infinite commutative ring under addition modulo 1 and usual product with infinite number of zero divisors and the ring has no unit element. We define multiset NC semigroup using the four intervals. Finally, we define n-multiplicity multiset NC semigroup for finite n and these two structures are semigroups under + modulo 1 and { M ( S ) , + , × } and { n - M ( S ) , + , × } are NC multiset semirings. Several interesting properties are discussed about these structures.

Fuzzy Lattice Ordered G-modules

2019 ◽  
Vol 8 (3) ◽  
pp. 94-107
Author(s):  
Ursala Paul ◽  
Paul Isaac
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set Theory ◽  
Real Life ◽  
Uncertain Information ◽  
Algebraic Structures ◽  
Ordered Groups ◽  
Lattice Ordered Groups ◽  
Fuzzy Lattice ◽  
Novel Concept

The study of mathematics emphasizes precision, accuracy, and perfection, but in many of the real-life situations, people face ambiguity, vagueness, imprecision, etc. Fuzzy set theory and rough set theory are two innovative tools in mathematics which are used for decision-making in vague and uncertain information systems. Fuzzy algebra has a significant role in the current era of mathematical research and it deals with the algebraic concepts and models of fuzzy sets. The study of various ordered algebraic structures like lattice ordered groups, Riesz spaces, etc., are of great importance in algebra. The theory of lattice ordered G-modules is very useful in the study of lattice ordered groups and similar algebraic structures. In this article, the theories of fuzzy sets and lattice ordered G-modules are synchronized in a suitable manner to evolve a novel concept in mathematics i.e., fuzzy lattice ordered G-modules which would pave the way for new researchers in fuzzy mathematics to explore much more in this field.

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