On Neutrosophic Sets And Topology
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| Author | : FRANCISCO GALLEGO LUPIAÑEZ |
| Publisher | : Infinite Study |
| Total Pages | : 9 |
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Recently, F.Smarandache generalized the Atanassov's intuitionistic fuzzy sets and other kinds of sets to neutrosophic sets. Also, this author defined the notion of neutrosophic topology on the non-standard interval. One can expect some relation between the intuitionistic fuzzy topology on an IFS and the neutrosophic topology. We show in this work that this is false.
| Author | : A. A. Salama |
| Publisher | : Infinite Study |
| Total Pages | : 4 |
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In this paper we introduce definitions of generalized neutrosophic sets. After given the fundamental definitions of generalized neutrosophic set operations, we obtain several properties, and discussed the relationship between generalized neutrosophic sets and others. Finally, we extend the concepts of neutrosophic topological space [9], intuitionistic fuzzy topological space [5, 6], and fuzzy topological space [4] to the case of generalized neutrosophic sets. Possible application to GIS topology rules are touched upon.
| Author | : Mohammed A. Al Shumrani |
| Publisher | : Infinite Study |
| Total Pages | : 14 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
For the first time we introduce non-standard neutrosophic topology on the extended non-standard analysis space, called non-standard real monad space, which is closed under neutrosophic non-standard infimum and supremum. Many classical topological concepts are extended to the non-standard neutrosophic topology, several theorems and properties about them are proven, and many examples are presented.
| Author | : Kalaivani Chandran |
| Publisher | : Infinite Study |
| Total Pages | : 20 |
| Release | : 2020-09-21 |
| Genre | : Mathematics |
| ISBN | : |
In this paper, we develop the notion of the basis for a smooth neutrosophic topology in a more natural way. As a sequel, we define the notion of symmetric neutrosophic quasi-coincident neighborhood systems and prove some interesting results that fit with the classical ones, to establish the consistency of theory developed. Finally, we define and discuss the concept of product topology, in this context, using the definition of basis.
| Author | : Mary Margaret A. |
| Publisher | : Infinite Study |
| Total Pages | : 12 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
The term topology was introduced by Johann Beredict Listing in the 19th century. Closed sets are fundamental objects in a topological space. In this paper, we use neutrosophic vague sets and topological spaces and we construct and develop a new concept namely “neutrosophic vague topological spaces”. By using the fundamental definition and necessary example we have defined the neutrosophic vague topological spaces and have also discussed some of its properties. Also we have defined the neutrosophic vague continuity and neutrosophic vague compact space in neutrosophic vague topological spaces and their properties are deliberated.
| Author | : N. Raksha Ben |
| Publisher | : Infinite Study |
| Total Pages | : 19 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
In this disquisition we have scrutinize about the traits of generalized topological spaces using neutrosophic sets. Depending on the nature of neutrosophic sets over the generalized topological spaces, some of the features has been contemplated.
| Author | : M. Lellis Thivagar |
| Publisher | : Infinite Study |
| Total Pages | : 10 |
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In this paper we desire to extend the neutrosophic topological spaces into N-neutrosophic topological spaces. Also we show that this theory can be deduced to N-intuitionistic and N-fuzzy topological spaces etc.
| Author | : P Evanzalin Ebenanjar |
| Publisher | : Infinite Study |
| Total Pages | : 6 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
Smarandache proposed the approach of neutrosophic sets. Neutrosophic sets deals with uncertain data. This paper de nes the notion of neutrosophic b-open sets and neutrosophic b-closed sets and their properties are investigated. Further neutrosphic b-interior and neutrosphic b-closure operators are studied and their relationship with other operators are also discussed.
| Author | : Francisco Gallego Lupiáñez |
| Publisher | : Infinite Study |
| Total Pages | : 6 |
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In 2005, Smarandache generalized the Atanassov’s intuitionistic fuzzy sets (IFSs) to neutrosophic sets (NS), and other researchers introduced the notion of interval neutrosophic set (INSs), which is an instance of NS, and studied various properties. The notion of neutrosophic topology on the non-standard interval is also due to Smarandache. The purpose of this paper is to study relations between INSs and topology.
| Author | : Wadei Al-Omeri |
| Publisher | : Infinite Study |
| Total Pages | : 21 |
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In Geographical information systems (GIS) there is a need to model spatial regions with indeterminate boundary and under indeterminacy. The purpose of this chapter is to construct the basic concepts of the so-called "neutrosophic sets via neutrosophic topological spaces (NTs)".
