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.

Neutrosophic Multigroup Homomorphism and Some of its Properties

2021 ◽  
pp. 110-126
Author(s):  
Memet Sahin ◽  
Keyword(s):  
Group Theory ◽  
Set Theory ◽  
Homomorphic Image ◽  
Fuzzy Set ◽  
Algebraic Structure ◽  
Fuzzy Set Theory ◽  
Classical Group ◽  
Elementary Theory ◽  
Group Structure ◽  
Basic Properties

In a way, the notion of neutrosophic multigroup is an application of neutrosophic multisets to the theory of group. The concept of neutrosophic multigroup is an algebraic structure of neutrosophic multiset that generalizes both the theories of classical group and neutrosophic group. Neutrosophic multigroup constitutes an application of neutrosophic multiset to the elementary theory of classical group. In this paper, we propose the concept of homomorphism on neutrosophic multigroup. We define homomorphism kerlf, automorphism, homomorphic image and homomorphic preimage of neutrosophic multigroup, respectively. Some homomorphic properties of neutrosophic multigroup are explicated. Some homomorphic properties of neutrosophic multigroup are also discussed. This new concept of homomorphism as a bridge among set theory, fuzzy set theory, neutrosophic multiset theory and group theory and also shows the effect of neutrosophic multisets on a group structure. We finally derive the basic properties of neutrosophic multigroup homomorphism and give its applications to group theory

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.

scholarly journals On the associativity property of MPF over M16

2018 ◽  
Vol 59 ◽  
pp. 7-12
Author(s):  
Aleksejus Mihalkovich
Keyword(s):  
Power Function ◽  
Algebraic Structure ◽  
Interesting Problem ◽  
Algebraic Structures ◽  
Basic Properties ◽  
Matrix Power ◽  
One Way Function ◽  
Future Work

The objective of this paper is to find suitable non-commuting algebraic structure to be used as a platform structure in the so-called matrix power function (MPF). We think it is non-trivial and interesting problem could be useful for candidate one-way function (OWF) construction with application in cryptography. Since the cornerstone of OWF construction using non-commuting algebraic structures is the satisfiability of certain associativity conditions, we consider one of the possible choices, i.e. the group M16, explore its basic properties and construct templates to use in our future work. 

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 Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 321 ◽  
Author(s):  
Mehmet Çelik ◽  
Moges Shalla ◽  
Necati Olgun
Keyword(s):  
Group Theory ◽  
Significant Role ◽  
Classical Group ◽  
Algebraic Structures ◽  
Algebraic Systems ◽  
Homomorphism Theorem ◽  
Special Cases ◽  
Isomorphism Theorems

In classical group theory, homomorphism and isomorphism are significant to study the relation between two algebraic systems. Through this article, we propose neutro-homomorphism and neutro-isomorphism for the neutrosophic extended triplet group (NETG) which plays a significant role in the theory of neutrosophic triplet algebraic structures. Then, we define neutro-monomorphism, neutro-epimorphism, and neutro-automorphism. We give and prove some theorems related to these structures. Furthermore, the Fundamental homomorphism theorem for the NETG is given and some special cases are discussed. First and second neutro-isomorphism theorems are stated. Finally, by applying homomorphism theorems to neutrosophic extended triplet algebraic structures, we have examined how closely different systems are related.

scholarly journals Some Results on Multigranulation Neutrosophic Rough Sets on a Single Domain

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 417 ◽  
Author(s):  
Hu Zhao ◽  
Hong-Ying Zhang
Keyword(s):  
Algebraic Structure ◽  
Rough Sets ◽  
Lattice Structure ◽  
Single Domain ◽  
One Dimensional ◽  
Basic Properties ◽  
Approximation Operators ◽  
Rough Approximation ◽  
The One ◽  
Comprehensive Study

As a generalization of single value neutrosophic rough sets, the concept of multi-granulation neutrosophic rough sets was proposed by Bo et al., and some basic properties of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators were studied. However, they did not do a comprehensive study on the algebraic structure of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators. In the present paper, we will provide the lattice structure of the pessimistic multigranulation neutrosophic rough approximation operators. In particular, in the one-dimensional case, for special neutrosophic relations, the completely lattice isomorphic relationship between upper neutrosophic rough approximation operators and lower neutrosophic rough approximation operators is proved.

scholarly journals Fuzzy Soft Multiset Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Abdul Razak Salleh
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Soft Set ◽  
Mathematical Tool ◽  
Basic Properties ◽  
Definition Of

In 1999 Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. Alkhazaleh et al. in 2011 introduced the definition of a soft multiset as a generalization of Molodtsov's soft set. In this paper we give the definition of fuzzy soft multiset as a combination of soft multiset and fuzzy set and study its properties and operations. We give examples for these concepts. Basic properties of the operations are also given. An application of this theory in decision-making problems is shown.

An approach to fuzzy multi-ideals of near rings

2021 ◽  
pp. 1-11
Author(s):  
Madeline Al Tahan ◽  
Sarka Hoskova-Mayerova ◽  
Bijan Davvaz
Keyword(s):  
Algebraic Structure ◽  
Algebraic Structures

In recent years, fuzzy multisets have become a subject of great interest for researchers and have been widely applied to algebraic structures including groups, rings, and many other algebraic structures. In this paper, we introduce the algebraic structure of fuzzy multisets as fuzzy multi-subnear rings (multi-ideals) of near rings. In this regard, we define different operations on fuzzy multi-ideals of near rings and we generalize some results known for fuzzy ideals of near rings to fuzzy multi-ideals of near rings.

Zur Formalisierung gruppendynamischer Konzepte / Inquiries in formalizing group-dynamic concepts

1975 ◽  
Vol 4 (2) ◽  
Author(s):  
Bruno Meile
Keyword(s):  
Set Theory ◽  
Group Structure ◽  
Frame Of Reference ◽  
Group Dynamic ◽  
Descriptive Model ◽  
Group Research ◽  
Basic Frame ◽  
The Stability

AbstractThe author tries to establish a formal-descriptive model for group-dynamic concepts in related logical terms and set theory. Cybernetics form the basic frame of reference. Herewith some fundamental principles such as ‘group’, ‘group structure’ and ‘change of group structure’ are defined exactly. - The consequences for empirical group research are shown by some examples: (1) a possible way out of the ‘methodological dilemma’ in sociometry,(2) a design for empirical description of the changes in group structure, (3) the formalization of a group-dynamic theorem, whereby groups of friends form according to the principle of individuals who share the same attributes. (4) The reshaping of the theorem allows the deduction of exact terminological hypotheses. New hypotheses, concerning the stability of group structure, can be gained through consideration of the cybernetic implications.

scholarly journals Logic and Truth: Some Logics without Theorems

2008 ◽  
pp. 104-117
Author(s):  
Jayanta Sen ◽  
Mihir Kumar Chakraborty
Keyword(s):  
Algebraic Structure ◽  
Logical Consequence ◽  
The Other ◽  
Algebraic Structures ◽  
Sequent Calculi

Two types of logical consequence are compared: one, with respect to matrix and designated elements and the other with respect to ordering in a suitable algebraic structure. Particular emphasis is laid on algebraic structures in which there is no top-element relative to the ordering. The significance of this special condition is discussed. Sequent calculi for a number of such structures are developed. As a consequence it is re-established that the notion of truth as such, not to speak of tautologies, is inessential in order to define validity of an argument.

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