A Study on Neutro-Topological Neighbourhood and Neutro-Topological Base

A Study on Neutro-Topological Neighbourhood and Neutro-Topological Base

Bhimraj Basumatary, Alympica Talukdar
Copyright: © 2023 |Pages: 15
DOI: 10.4018/978-1-6684-4740-6.ch009
OnDemand:
(Individual Chapters)
Available
$37.50
Current Special Offers
No Current Special Offers
TOTAL SAVINGS: $37.50

Abstract

Recently, Smarandache introduced NeutroAlgebra and AntiAlgebras. NeutroAlgebras and AntiAlgebras represent a new research subject that is based on real-world examples. He studied the concept of neutro-structures and anti-structures. From the concepts of NeutroAlgebra, he showed that if a statement (theorem, lemma, consequence, property, etc.) is totally true in a classical Algebra, it does not mean that it is also totally true in a NeutroAlgebra or an AntiAlgebra. It depends on the operations and axioms (if they are totally true, partially true, totally false, or partially or totally indeterminate) it is based upon. In this study, the concept of Neutro-Topological neighbourhood and Neutro-Topological base are studied. Some examples of Neutro-Neighbourhood and Neutro-Base are given and compare the results of classical topological neighbourhood and Neutro-Topological Neighbourhood as well as classical topological base and Neutro-Topological Base.
Chapter Preview
Top

Preliminaries

Definition 1. (Smarandache, 2020c) The NeutroSophication of the Law

  • (i)

    Let X be a non-empty set and * be a binary operation. For some elements (a,b)∈(X,X), (a*b)∈X (degree of well defined (T)) and for other elements (x,y),(p,q)∈(X,X); [x*y is indeterminate (degree of indeterminacy (I)), or p*q∉X (degree of outer-defined (F)], where (T, I, F) is different from (1,0,0) that represents the Classical Law, and from (0,0,1) that represents the AntiLaw.

  • (ii)

    In Neutro Algebra, the classical well-defined for binary operation * is divided into three regions: degree of well-defined (T), degree of indeterminacy (I) and degree of outer-defined (F) similar to neutrosophic set and neutrosophic logic.

Complete Chapter List

Search this Book:
Reset