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Search Results (4)

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Keywords = special neutrosophic triplets

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22 pages, 1911 KB  
Article
On Neutrosophic Extended Triplet LA-hypergroups and Strong Pure LA-semihypergroups
by Minghao Hu, Florentin Smarandache and Xiaohong Zhang
Symmetry 2020, 12(1), 163; https://doi.org/10.3390/sym12010163 - 14 Jan 2020
Cited by 5 | Viewed by 2775
Abstract
We introduce the notions of neutrosophic extended triplet LA-semihypergroup, neutrosophic extended triplet LA-hypergroup, which can reflect some symmetry of hyperoperation and discuss the relationships among them and regular LA-semihypergroups, LA-hypergroups, regular LA-hypergroups. In particular, we introduce the notion of strong pure neutrosophic extended [...] Read more.
We introduce the notions of neutrosophic extended triplet LA-semihypergroup, neutrosophic extended triplet LA-hypergroup, which can reflect some symmetry of hyperoperation and discuss the relationships among them and regular LA-semihypergroups, LA-hypergroups, regular LA-hypergroups. In particular, we introduce the notion of strong pure neutrosophic extended triplet LA-semihypergroup, get some special properties of it and prove the construction theorem about it under the condition of asymmetry. The examples in this paper are all from Python programs. Full article
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9 pages, 731 KB  
Article
Neutrosophic Triplets in Neutrosophic Rings
by Vasantha Kandasamy W. B., Ilanthenral Kandasamy and Florentin Smarandache
Mathematics 2019, 7(6), 563; https://doi.org/10.3390/math7060563 - 20 Jun 2019
Cited by 15 | Viewed by 3212
Abstract
The neutrosophic triplets in neutrosophic rings ⟨ Q ∪ I ⟩ and ⟨ R ∪ I ⟩ are investigated in this paper. However, non-trivial neutrosophic triplets are not found in ⟨ Z ∪ I ⟩ . In the neutrosophic ring of integers [...] Read more.
The neutrosophic triplets in neutrosophic rings ⟨ Q ∪ I ⟩ and ⟨ R ∪ I ⟩ are investigated in this paper. However, non-trivial neutrosophic triplets are not found in ⟨ Z ∪ I ⟩ . In the neutrosophic ring of integers Z \ { 0 , 1 } , no element has inverse in Z. It is proved that these rings can contain only three types of neutrosophic triplets, these collections are distinct, and these collections form a torsion free abelian group as triplets under component wise product. However, these collections are not even closed under component wise addition. Full article
(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)
14 pages, 786 KB  
Article
Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups
by Mehmet Çelik, Moges Mekonnen Shalla and Necati Olgun
Symmetry 2018, 10(8), 321; https://doi.org/10.3390/sym10080321 - 3 Aug 2018
Cited by 9 | Viewed by 4200
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets)
7 pages, 688 KB  
Article
Fixed Point Theorem for Neutrosophic Triplet Partial Metric Space
by Memet Şahin, Abdullah Kargın and Mehmet Ali Çoban
Symmetry 2018, 10(7), 240; https://doi.org/10.3390/sym10070240 - 25 Jun 2018
Cited by 18 | Viewed by 3861
Abstract
Neutrosphic triplet is a new theory in neutrosophy. In a neutrosophic triplet set, there is a neutral element and antielement for each element. In this study, the concept of neutrosophic triplet partial metric space (NTPMS) is given and the properties of NTPMS are [...] Read more.
Neutrosphic triplet is a new theory in neutrosophy. In a neutrosophic triplet set, there is a neutral element and antielement for each element. In this study, the concept of neutrosophic triplet partial metric space (NTPMS) is given and the properties of NTPMS are studied. We show that both classical metric and neutrosophic triplet metric (NTM) are different from NTPM. Also, we show that NTPMS can be defined with each NTMS. Furthermore, we define a contraction for NTPMS and we give a fixed point theory (FPT) for NTPMS. The FPT has been revealed as a very powerful tool in the study of nonlinear phenomena. This study is also part of the “Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets” which is a special issue. Full article
(This article belongs to the Special Issue Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets)
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