International Journal of Neutrosophic Science
IJNS
2690-6805
2692-6148
10.54216/IJNS
https://www.americaspg.com/journals/show/2355
2020
2020
Neutrosophic Topological Vector Spaces and its Properties
Sakthi Institute of Information and Management Studies, Pollachi, Coimbatore, Tamil Nadu - 642001, India
E.
Kungumaraj
Akshaya College of Engineering and Technology, Kinathukadavu, Coimbatore, Tamil Nadu - 642109, India
E.
Lathanayagam
Department of Mathematics, Silapathar College, Dhemaji, Assam – 787059, India
Utpal
Saikia
Department of Mathematics, Mount Carmel College (Autonomous), Affiliated to Bengaluru City University, Bengaluru - 560052, Karnataka, India
M. Clement Joe
Anand
Department of Computer Science, Ram Lal Anand College, University of Delhi- 110021, Delhi, India
Sakshi Taaresh
Khanna
Department of Mathematics, Arul Anandar College (Autonomous), Karumathur-625514, Tamil Nadu, India
Nivetha
Martin
Department of Computer Science and Engineering, Bharati Vidyapeeth’s College of Engineering, Delhi -110063, Delhi, India
Mohit
Tiwari
Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran
Seyyed Ahmad
Edalatpanah
The algebraic structures Group, Ring, Field and Vector spaces are important innovations in Mathematics. Most of the theoretical concepts of Mathematics are based on the theorems related to these algebraic structures. Initially many mathematicians developed theorems related to all these algebraic structures. In 20th century most of the researchers introduced the theorems on the algebraic structures with Fuzzy and Intuitionistic fuzzy sets. Recently in 21st century the researchers concentrated on Neutrosophic sets and introduced the algebraic structures like Neutrosophic Group, Neutrosophic Ring, Neutrosophic Field, Neutrosophic Vector spaces and Neutrosophic Linear Transformation. In the current scenario of relating the spaces with the structures, we have introduced the concepts of Neutrosophic topological vector spaces. In this article, the study of Neutrosophic Topological vector spaces has been initiated. Some basic definitions and properties of classical vector spaces are generalized in Neutrosophic environment over a Neutrosophic field with continuous functions. Neutrosophic linear transformations and their properties are also included in Neutrosophic Topological Vector spaces. This article is an extension work of fuzzy and intuitionistic fuzzy vector spaces which were introduced in fuzzy and intuitionistic fuzzy environments. Even though it is an extension work, Neutrosophic Topological Vector space will play an important role in Neural Networks, Image Processing, Machine Learning and Artificial Intelligence Algorithms.
2024
2024
63
76
10.54216/IJNS.230206
https://www.americaspg.com/articleinfo/21/show/2355