A New Approach To Operations On Neutrosophic Soft Sets And To Neutrosophic Soft Topological Spaces
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| Author | : Taha Yasin Ozturk |
| Publisher | : Infinite Study |
| Total Pages | : 13 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
In this study, we re-define some operations on neutrosophic soft sets differently from the studies [3, 9]. On this operations are given interesting examples and them basic properties. In the direction of these newly defined operations, we construct the neutrosophic soft topological spaces differently from the study [3]. Finally, we introduce basic definitions and theorems on neutrosophic soft topological spaces.
| Author | : Taha Yasin Ozturk |
| Publisher | : Infinite Study |
| Total Pages | : 12 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
In this study, we re-define some operations on bipolar neutrosophic soft sets differently from the studies. On this operations are given interesting examples and them basic properties. In the direction of these newly defined operations, we construct the bipolar neutrosophic soft topological spaces. Finally, we introduce basic definitions and theorems on bipolar neutrosophic soft topological spaces.
| Author | : Ahmed B. Al-Nafee |
| Publisher | : Infinite Study |
| Total Pages | : 15 |
| Release | : 2020-12-01 |
| Genre | : Mathematics |
| ISBN | : |
The goal of this paper is to study and discuss the neutrosophic soft set theory by introducing, new family of neutrosophic soft sets and because the concept of topological spaces is one of the most powerful concepts in system analysis, we introduced the concept of neutrosophic soft topological spaces depending on this the new family. Furthermore, we introduced new definitions, properties, concerning the neutrosophic soft closuer, the neutrosophic soft interior, the neutrosophic soft exterior and the neutrosophic soft boundary in details of neutrosophic compact. We prove that for a countable neutrosophic-space X: countably compactness and compactness are equivalent. We give an example of a neutrosophic space X which has a neutrosophic countable base but it is not neutrosophic countably compact.
| Author | : Tuhin Bera |
| Publisher | : Infinite Study |
| Total Pages | : 13 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
In this paper, the concept of connectedness and compactness on neutrosophic soft topological space have been introduced along with the investigation of their several characteristics. Some related theorems have been established also.
| Author | : Pabitra Kumar Maji |
| Publisher | : Infinite Study |
| Total Pages | : 12 |
| Release | : |
| Genre | : |
| ISBN | : |
In this paper we study the concept of neutrosophic set of Smarandache. We have introduced this concept in soft sets and defined neutrosophic soft set. Some definitions and operations have been introduced on neutrosophic soft set. Some properties of this concept have been established.
| Author | : Somen Debnath |
| Publisher | : Infinite Study |
| Total Pages | : 8 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
Earlier fuzzy set, vague set, intuitionistic fuzzy set, L-fuzzy set etc are used as a mathematical tools for solving problems based on uncertainties or ambiguous in nature. But due to more complexity involves in problems exist in nature, traditional tools are unable to handle those in a systematic manner. So we need a tool which is more flexible to handle those problems. Which leads to the invention of soft set which was introduced by Molodtsov in 1999. Soft set (SS) theory is a mathematical tool deals with parametric data which are imprecise in nature. Ithis a generalization of fuzzy set theory. On the other hand Rough set (RS) theory and Neutrosophic set (NS) theory both rising as a powerful tool to handle these uncertain, incomplete, inconsistent and imprecise information in an effective manner. Actually Neutrosophic set is a generalization of intuitionistic fuzzy set. Sometimes it is not possible to handle all sorts of uncertain problems with a single mathematical tool. Fusion of two or more mathematical tools give rise to a new mathematical concept which gives an idea how to solve such type of problems in a more sophisticated ways. Which leads to the introduction of fuzzy soft set, rough soft set, intuitionistic fuzzy soft set, soft rough set etc. Neutrosophic soft set (NSS) was established by combining the concept of Soft set and Neutrosophic set. In this paper, using the concept of Rough set and Neutrosophic soft set a new concept known as Rough neutrosophic soft set (RNSS) is developed. Some properties and operations on them are introduced.
| Author | : Arif Mehmood |
| Publisher | : Infinite Study |
| Total Pages | : 15 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
In this article, new generalised neutrosophic soft open known as neutrosophic soft ∗b-open set is introduced in neutrosophic soft topological spaces. Neutrosophic soft ∗b-open set is generated with the help of neutrosophic soft semiopen and neutrosophic soft preopen sets.
| Author | : Arif Mehmood |
| Publisher | : Infinite Study |
| Total Pages | : 31 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
In this paper, the notion of generalized neutrosophic soft open set (GNSOS) in neutrosophic soft open set (GNSOS) in neutrosophic soft topological structures relative to neutrosophic soft points is introduced.
| Author | : Arif Mehmood Khattak |
| Publisher | : Infinite Study |
| Total Pages | : 13 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
The idea of neutrosophic set was floated by Smarandache by supposing a truth membership, an indeterminacy membership and a falsehood or falsity membership functions. Neutrosophic soft sets bonded by Maji have been utilized successfully to model uncertainty in several areas of application such as control, reasoning, pattern recognition and computer vision. The rst aim of this article bounces the idea of neutrosophic soft b-open set, neutrosophic soft b-closed sets and their properties.Also the idea of neutrosophic soft b-neighborhood and neutrosophic soft b-separation axioms in neutrosophic soft topological structures are also reflected here.
| Author | : Ashraf Al-Quran |
| Publisher | : Infinite Study |
| Total Pages | : 16 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
To handle indeterminate and incomplete data, neutrosophic logic/set/probability were established. The neutrosophic truth, falsehood and indeterminacy components exhibit symmetry as the truth and the falsehood look the same and behave in a symmetrical way with respect to the indeterminacy component which serves as a line of the symmetry. Soft set is a generic mathematical tool for dealing with uncertainty. Rough set is a new mathematical tool for dealing with vague, imprecise, inconsistent and uncertain knowledge in information systems. This paper introduces a new rough set model based on neutrosophic soft set to exploit simultaneously the advantages of rough sets and neutrosophic soft sets in order to handle all types of uncertainty in data. The ideaof neutrosophic right neighborhood is utilised to define the concepts of neutrosophic soft rough (NSR) lower and upper approximations. Properties of suggested approximations are proposed and subsequently proven. Some of the NSR set concepts such as NSR-definability, NSR-relations and NSR-membership functions are suggested and illustrated with examples. Further, we demonstrate the feasibility of the newly rough set model with decision making problems involving neutrosophic soft set. Finally, a discussion on the features and limitations of the proposed model is provided.
